diff --git a/src/sage/algebras/quantum_clifford.py b/src/sage/algebras/quantum_clifford.py
index 1e57682f255..5079283e8ec 100644
--- a/src/sage/algebras/quantum_clifford.py
+++ b/src/sage/algebras/quantum_clifford.py
@@ -27,7 +27,7 @@
 from sage.rings.fraction_field import FractionField
 from sage.sets.finite_enumerated_set import FiniteEnumeratedSet
 from itertools import product
-from sage.misc.misc import powerset
+from sage.combinat.subset import powerset
 
 class QuantumCliffordAlgebra(CombinatorialFreeModule):
     r"""
diff --git a/src/sage/arith/misc.py b/src/sage/arith/misc.py
index d3b5d164054..c29005e03ba 100644
--- a/src/sage/arith/misc.py
+++ b/src/sage/arith/misc.py
@@ -20,7 +20,6 @@
 import math
 from collections.abc import Iterable
 
-from sage.misc.misc import powerset
 from sage.misc.misc_c import prod
 
 from sage.structure.element import parent
@@ -6042,6 +6041,8 @@ def squarefree_divisors(x):
         sage: list(squarefree_divisors(mpz(12)))
         [1, 2, 3, 6]
     """
+    from sage.combinat.subset import powerset
+
     for a in powerset(prime_divisors(x)):
         yield prod(a, ZZ.one())
 
diff --git a/src/sage/categories/coxeter_groups.py b/src/sage/categories/coxeter_groups.py
index 95c31d20695..4cb0b21d7a1 100644
--- a/src/sage/categories/coxeter_groups.py
+++ b/src/sage/categories/coxeter_groups.py
@@ -1327,7 +1327,10 @@ def _test_coxeter_relations(self, **options):
             one = self.one()
             for si in s:
                 tester.assertEqual(si**2, one)
-            cox_mat = self.coxeter_matrix()
+            try:
+                cox_mat = self.coxeter_matrix()
+            except ImportError:
+                return
             I = cox_mat.index_set()
             for ii, i in enumerate(I):
                 for j in I[ii + 1:]:
diff --git a/src/sage/categories/finite_coxeter_groups.py b/src/sage/categories/finite_coxeter_groups.py
index 0ec68ca2b99..a03a7ca5495 100644
--- a/src/sage/categories/finite_coxeter_groups.py
+++ b/src/sage/categories/finite_coxeter_groups.py
@@ -10,6 +10,8 @@
 #                  https://www.gnu.org/licenses/
 # *****************************************************************************
 
+import sage.rings.abc
+
 from sage.misc.cachefunc import cached_method, cached_in_parent_method
 from sage.misc.lazy_attribute import lazy_attribute
 from sage.categories.category_with_axiom import CategoryWithAxiom
@@ -746,13 +748,14 @@ def permutahedron(self, point=None, base_ring=None):
                 from sage.rings.integer_ring import ZZ
                 point = [ZZ.one()] * n
             v = sum(point[i-1] * weights[i] for i in weights.keys())
-            from sage.geometry.polyhedron.constructor import Polyhedron
-            from sage.rings.qqbar import AA, QQbar
-            from sage.rings.universal_cyclotomic_field import UniversalCyclotomicField
             vertices = [v*w for w in self]
-            if base_ring is None and v.base_ring() in [UniversalCyclotomicField(), QQbar]:
-                vertices = [v.change_ring(AA) for v in vertices]
-                base_ring = AA
+            if base_ring is None:
+                if isinstance(v.base_ring(), (sage.rings.abc.UniversalCyclotomicField,
+                                              sage.rings.abc.AlgebraicField_common)):
+                    from sage.rings.qqbar import AA
+                    vertices = [v.change_ring(AA) for v in vertices]
+                    base_ring = AA
+            from sage.geometry.polyhedron.constructor import Polyhedron
             return Polyhedron(vertices=vertices, base_ring=base_ring)
 
     class ElementMethods:
diff --git a/src/sage/categories/loop_crystals.py b/src/sage/categories/loop_crystals.py
index b7dbd37a3c6..2d5f1ca1914 100644
--- a/src/sage/categories/loop_crystals.py
+++ b/src/sage/categories/loop_crystals.py
@@ -968,7 +968,7 @@ def energy_function(self, algorithm=None):
                     ....:     for b in hw)
                     True
                 """
-                from sage.functions.other import ceil
+                from sage.arith.misc import integer_ceil as ceil
 
                 C = self.parent().crystals[0]
                 ell = ceil(C.s()/C.cartan_type().c()[C.r()])
@@ -1101,7 +1101,7 @@ def e_string_to_ground_state(self):
                     ....:     for elt in hw)
                     True
                 """
-                from sage.functions.other import ceil
+                from sage.arith.misc import integer_ceil as ceil
 
                 ell = max(ceil(K.s()/K.cartan_type().c()[K.r()])
                           for K in self.parent().crystals)
diff --git a/src/sage/combinat/all.py b/src/sage/combinat/all.py
index 2206ea2873a..0f43e6bbcfe 100644
--- a/src/sage/combinat/all.py
+++ b/src/sage/combinat/all.py
@@ -218,7 +218,7 @@
 lazy_import('sage.combinat.multiset_partition_into_sets_ordered',
             ['OrderedMultisetPartitionIntoSets',
              'OrderedMultisetPartitionsIntoSets'])
-from .subset import Subsets
+from .subset import Subsets, subsets, powerset, uniq
 from .necklace import Necklaces
 lazy_import('sage.combinat.dyck_word', ('DyckWords', 'DyckWord'))
 lazy_import('sage.combinat.nu_dyck_word', ('NuDyckWords', 'NuDyckWord'))
diff --git a/src/sage/combinat/blob_algebra.py b/src/sage/combinat/blob_algebra.py
index 95899fd66a6..657c70a5c0e 100644
--- a/src/sage/combinat/blob_algebra.py
+++ b/src/sage/combinat/blob_algebra.py
@@ -23,7 +23,7 @@
 from sage.structure.richcmp import richcmp
 #from sage.misc.inherit_comparison import InheritComparisonClasscallMetaclass
 from sage.misc.cachefunc import cached_method
-from sage.misc.misc import powerset
+from sage.combinat.subset import powerset
 from sage.arith.misc import binomial
 from sage.categories.finite_enumerated_sets import FiniteEnumeratedSets
 from sage.categories.algebras import Algebras
diff --git a/src/sage/combinat/combinat.py b/src/sage/combinat/combinat.py
index 195ff344e50..5d27891dee0 100644
--- a/src/sage/combinat/combinat.py
+++ b/src/sage/combinat/combinat.py
@@ -64,18 +64,12 @@
 
 **Implemented in other modules (listed for completeness):**
 
-The ``sage.arith.all`` module contains the following
+The package :mod:`sage.arith` contains the following
 combinatorial functions:
 
--  binomial the binomial coefficient (wrapped from PARI)
+-  :func:`binomial` the binomial coefficient (wrapped from PARI)
 
--  factorial (wrapped from PARI)
-
--  partition (from the Python Cookbook) Generator of the list of
-   all the partitions of the integer `n`.
-
--  :func:`number_of_partitions` (wrapped from PARI) the
-   *number* of partitions:
+-  :func:`factorial` (wrapped from PARI)
 
 -  :func:`falling_factorial` Definition: for integer
    `a \ge 0` we have `x(x-1) \cdots (x-a+1)`. In all
@@ -87,7 +81,12 @@
    other cases we use the GAMMA-function:
    `\frac {\Gamma(x+a)} {\Gamma(x)}`.
 
--  gaussian_binomial the gaussian binomial
+From other modules:
+
+-  :func:`number_of_partitions` (wrapped from PARI) the
+   *number* of partitions:
+
+-  :func:`sage.combinat.q_analogues.gaussian_binomial` the Gaussian binomial
 
 .. MATH::
 
@@ -174,8 +173,6 @@
 from sage.rings.infinity import infinity
 from sage.rings.polynomial.polynomial_element import Polynomial
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-from sage.libs.pari.all import pari
-from sage.misc.prandom import randint
 from sage.misc.misc_c import prod
 from sage.misc.cachefunc import cached_function
 from sage.structure.sage_object import SageObject
@@ -187,7 +184,10 @@
 from sage.misc.classcall_metaclass import ClasscallMetaclass
 from sage.misc.inherit_comparison import InheritComparisonClasscallMetaclass
 from sage.structure.element import Element
+
 lazy_import('sage.interfaces.maxima_lib', 'maxima')
+lazy_import('sage.libs.pari.all', 'pari')
+lazy_import('sage.misc.prandom', 'randint')
 
 
 def bell_number(n, algorithm='flint', **options) -> Integer:
@@ -2892,7 +2892,7 @@ def unshuffle_iterator(a, one=1) -> Iterator:
         [(((), (3, 1)), 3/2), (((3,), (1,)), 3/2), (((1,), (3,)), -3/2),
          (((3, 1), ()), 3/2)]
     """
-    from sage.misc.misc import powerset
+    from sage.combinat.subset import powerset
     n = len(a)
     for I in powerset(range(n)):
         sorted_I = tuple(sorted(I))
diff --git a/src/sage/combinat/designs/bibd.py b/src/sage/combinat/designs/bibd.py
index 2265e113040..071c1db387e 100644
--- a/src/sage/combinat/designs/bibd.py
+++ b/src/sage/combinat/designs/bibd.py
@@ -50,12 +50,16 @@
 ---------
 """
 
+from sage.arith.misc import binomial, is_prime_power, is_square
 from sage.categories.sets_cat import EmptySetError
+from sage.misc.lazy_import import lazy_import
 from sage.misc.unknown import Unknown
+
 from .design_catalog import transversal_design  # type:ignore
-from sage.arith.misc import binomial, is_prime_power
-from .group_divisible_designs import GroupDivisibleDesign
 from .designs_pyx import is_pairwise_balanced_design
+from .group_divisible_designs import GroupDivisibleDesign
+
+lazy_import('sage.schemes.plane_conics.constructor', 'Conic')
 
 
 def biplane(n, existence=False):
@@ -413,8 +417,6 @@ def BruckRyserChowla_check(v, k, lambd):
         True
 
     """
-    from sage.arith.misc import is_square
-    from sage.schemes.plane_conics.constructor import Conic
     from sage.rings.rational_field import QQ
 
     # design is not symmetric
diff --git a/src/sage/combinat/designs/difference_family.py b/src/sage/combinat/designs/difference_family.py
index 52a95805ea5..fb510a83b0e 100644
--- a/src/sage/combinat/designs/difference_family.py
+++ b/src/sage/combinat/designs/difference_family.py
@@ -1530,7 +1530,6 @@ def relative_difference_set_from_homomorphism(q, N, d, check=True, return_group=
         return G2, second_diff_set
     return second_diff_set
 
-
 def is_relative_difference_set(R, G, H, params, verbose=False):
     r"""
     Check if ``R`` is a difference set of ``G`` relative to ``H``, with the given parameters.
@@ -2040,9 +2039,6 @@ def skew_supplementary_difference_set_over_polynomial_ring(n, existence=False, c
         ...
         NotImplementedError: skew SDS of order 7 not yet implemented
     """
-    from sage.symbolic.ring import SymbolicRing
-    from sage.rings.finite_rings.integer_mod_ring import Zmod
-
     data = {
         81: (3, lambda x: x**4 - x**3 - 1, 16, 5,
              [1, 2, 4, 6, 8, 10, 12, 14], [1, 2, 3, 4, 10, 11, 13],
@@ -2060,9 +2056,11 @@ def skew_supplementary_difference_set_over_polynomial_ring(n, existence=False, c
 
     mod, poly, exp, order, ind1, ind2, ind3, ind4 = data[n]
 
+    from sage.rings.finite_rings.integer_mod_ring import Zmod
+
     Z3 = Zmod(mod)
-    R = SymbolicRing()
-    x = R.var('x')
+    R = ZZ['x']
+    x = R.gen()
     F = Z3.extension(poly(x))
 
     H = [F.gen() ** (exp * i) for i in range(order)]
diff --git a/src/sage/combinat/designs/incidence_structures.py b/src/sage/combinat/designs/incidence_structures.py
index 1aa6c34d733..fbb003122ab 100644
--- a/src/sage/combinat/designs/incidence_structures.py
+++ b/src/sage/combinat/designs/incidence_structures.py
@@ -39,10 +39,13 @@
 #                    https://www.gnu.org/licenses/                          #
 # **************************************************************************
 from __future__ import annotations
-from sage.rings.integer import Integer
+
 from sage.misc.latex import latex
+from sage.misc.lazy_import import lazy_import
+from sage.rings.integer import Integer
 from sage.sets.set import Set
-from sage.libs.gap.libgap import libgap
+
+lazy_import('sage.libs.gap.libgap', 'libgap')
 
 
 class IncidenceStructure():
@@ -173,7 +176,6 @@ def __init__(self, points=None, blocks=None, incidence_matrix=None,
             sage: IncidenceStructure([])
             Incidence structure with 0 points and 0 blocks
         """
-        from sage.matrix.constructor import matrix
         from sage.structure.element import Matrix
 
         # Reformatting input
@@ -189,6 +191,7 @@ def __init__(self, points=None, blocks=None, incidence_matrix=None,
             assert incidence_matrix is None, "'incidence_matrix' cannot be defined when 'points' is defined"
 
         if incidence_matrix:
+            from sage.matrix.constructor import matrix
             M = matrix(incidence_matrix)
             v = M.nrows()
             self._points = list(range(v))
diff --git a/src/sage/combinat/diagram.py b/src/sage/combinat/diagram.py
index dcde71bff63..ed32713b5c2 100644
--- a/src/sage/combinat/diagram.py
+++ b/src/sage/combinat/diagram.py
@@ -615,7 +615,7 @@ def __iter__(self):
         """
         from sage.sets.non_negative_integers import NonNegativeIntegers
         from sage.categories.cartesian_product import cartesian_product
-        from sage.misc.misc import subsets
+        from sage.combinat.subset import subsets
         # the product of positive integers automatically implements an
         # an enumeration which allows us to get out of the first column
         N = NonNegativeIntegers()
diff --git a/src/sage/combinat/diagram_algebras.py b/src/sage/combinat/diagram_algebras.py
index bd281fdbb77..da6628ed840 100644
--- a/src/sage/combinat/diagram_algebras.py
+++ b/src/sage/combinat/diagram_algebras.py
@@ -231,7 +231,7 @@ def planar_partitions_rec(X):
         if len(X) > 1:
             yield ([X[0]], [X[1]])
         return
-    from sage.misc.misc import powerset
+    from sage.combinat.subset import powerset
     from itertools import product
     for S in powerset(range(len(X)-1)):
         if not S:
diff --git a/src/sage/combinat/integer_vector_weighted.py b/src/sage/combinat/integer_vector_weighted.py
index 1b110c34140..071c814f3bb 100644
--- a/src/sage/combinat/integer_vector_weighted.py
+++ b/src/sage/combinat/integer_vector_weighted.py
@@ -20,13 +20,15 @@
 from sage.categories.finite_enumerated_sets import FiniteEnumeratedSets
 from sage.categories.infinite_enumerated_sets import InfiniteEnumeratedSets
 from sage.categories.sets_with_grading import SetsWithGrading
+from sage.misc.lazy_import import lazy_import
 from sage.sets.disjoint_union_enumerated_sets import DisjointUnionEnumeratedSets
 from sage.rings.integer import Integer
 from sage.rings.integer_ring import ZZ
 from sage.combinat.integer_vector import IntegerVector
-from sage.combinat.words.word import Word
 from sage.combinat.permutation import Permutation
 
+lazy_import('sage.combinat.words.word', 'Word')
+
 
 class WeightedIntegerVectors(Parent, UniqueRepresentation):
     r"""
diff --git a/src/sage/combinat/interval_posets.py b/src/sage/combinat/interval_posets.py
index a2d4f6e607c..70b165befee 100644
--- a/src/sage/combinat/interval_posets.py
+++ b/src/sage/combinat/interval_posets.py
@@ -3042,7 +3042,13 @@ def final_forest(element) -> TIP:
         """
         if isinstance(element, TamariIntervalPoset):
             return element.final_forest()
-        if element in DyckWords():
+
+        try:
+            DW = DyckWords()
+        except ImportError:
+            DW = ()
+
+        if element in DW:
             binary_tree = element.to_binary_tree_tamari()
         elif element in BinaryTrees() or element in LabelledBinaryTrees():
             binary_tree = element
@@ -3149,7 +3155,13 @@ def initial_forest(element) -> TIP:
         """
         if isinstance(element, TamariIntervalPoset):
             return element.initial_forest()
-        if element in DyckWords():
+
+        try:
+            DW = DyckWords()
+        except ImportError:
+            DW = ()
+
+        if element in DW:
             binary_tree = element.to_binary_tree_tamari()
         elif element in BinaryTrees() or element in LabelledBinaryTrees():
             binary_tree = element
diff --git a/src/sage/combinat/permutation.py b/src/sage/combinat/permutation.py
index 9593055e9ed..4d7b3d09923 100644
--- a/src/sage/combinat/permutation.py
+++ b/src/sage/combinat/permutation.py
@@ -242,6 +242,7 @@
 from __future__ import annotations
 from typing import Iterator
 import itertools
+import operator
 
 from sage.arith.misc import factorial, multinomial
 from sage.categories.finite_enumerated_sets import FiniteEnumeratedSets
@@ -256,16 +257,10 @@
 from sage.combinat.permutation_cython import (left_action_product, right_action_product,
                                               left_action_same_n, right_action_same_n,
                                               map_to_list, next_perm)
-from sage.combinat.rsk import RSK, RSK_inverse
 from sage.combinat.tools import transitive_ideal
-from sage.graphs.digraph import DiGraph
-from sage.groups.perm_gps.permgroup_element import PermutationGroupElement
-from sage.groups.perm_gps.permgroup_named import SymmetricGroup
-from sage.libs.gap.libgap import libgap
-from sage.matrix.matrix_space import MatrixSpace
 from sage.misc.cachefunc import cached_method
 from sage.misc.decorators import rename_keyword
-from sage.misc.prandom import sample
+from sage.misc.lazy_import import lazy_import
 from sage.rings.integer import Integer
 from sage.rings.integer_ring import ZZ
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
@@ -274,7 +269,18 @@
 from sage.structure.parent import Parent
 from sage.structure.element import Element, get_coercion_model
 from sage.structure.unique_representation import UniqueRepresentation
-import operator
+
+lazy_import('sage.combinat.rsk', ['RSK', 'RSK_inverse'])
+lazy_import('sage.combinat.tableau', 'Tableau')
+lazy_import('sage.combinat.words.finite_word', 'evaluation_dict')
+lazy_import('sage.graphs.digraph', 'DiGraph')
+lazy_import('sage.groups.cactus_group', 'CactusGroup')
+lazy_import('sage.groups.perm_gps.permgroup_element', 'PermutationGroupElement')
+lazy_import('sage.groups.perm_gps.permgroup_named', 'SymmetricGroup')
+lazy_import('sage.libs.gap.libgap', 'libgap')
+lazy_import('sage.matrix.matrix_space', 'MatrixSpace')
+lazy_import('sage.misc.prandom', 'sample')
+
 
 class Permutation(CombinatorialElement):
     r"""
@@ -441,7 +447,6 @@ def __classcall_private__(cls, l, check=True):
             sage: P.parent()
             Standard permutations
         """
-        import sage.combinat.tableau as tableau
         if isinstance(l, Permutation):
             return l
         elif isinstance(l, PermutationGroupElement):
@@ -461,11 +466,11 @@ def __classcall_private__(cls, l, check=True):
 
         #if l is a pair of standard tableaux or a pair of lists
         elif isinstance(l, (tuple, list)) and len(l) == 2 and \
-            all(isinstance(x, tableau.Tableau) for x in l):
+            all(isinstance(x, Tableau) for x in l):
             return RSK_inverse(*l, output='permutation')
         elif isinstance(l, (tuple, list)) and len(l) == 2 and \
             all(isinstance(x, list) for x in l):
-            P,Q = [tableau.Tableau(_) for _ in l]
+            P,Q = [Tableau(_) for _ in l]
             return RSK_inverse(P, Q, 'permutation')
         # if it's a tuple or nonempty list of tuples, also assume cycle
         # notation
@@ -870,7 +875,6 @@ def to_tableau_by_shape(self, shape):
             sage: Permutation([3,4,1,2,5]).to_tableau_by_shape([3,2]).reading_word_permutation()
             [3, 4, 1, 2, 5]
         """
-        import sage.combinat.tableau as tableau
         if sum(shape) != len(self):
             raise ValueError("the size of the partition must be the size of self")
 
@@ -879,7 +883,7 @@ def to_tableau_by_shape(self, shape):
         for i in reversed(shape):
             t = [w[:i]] + t
             w = w[i:]
-        return tableau.Tableau(t)
+        return Tableau(t)
 
     def to_cycles(self, singletons=True, use_min=True):
         """
@@ -6924,7 +6928,6 @@ def _coerce_map_from_(self, G):
             return self._from_permutation_group_element
         if isinstance(G, StandardPermutations_n) and G.n <= self.n:
             return True
-        from sage.groups.cactus_group import CactusGroup
         if isinstance(G, CactusGroup) and G.n() <= self.n:
             return self._from_cactus_group_element
         return super()._coerce_map_from_(G)
@@ -8682,8 +8685,6 @@ def permutohedron_lequal(p1, p2, side="right"):
 ############
 # Patterns #
 ############
-from sage.combinat.words.finite_word import evaluation_dict
-
 
 def to_standard(p, key=None):
     r"""
diff --git a/src/sage/combinat/root_system/cartan_matrix.py b/src/sage/combinat/root_system/cartan_matrix.py
index 3a26227b4f1..77f175f0364 100644
--- a/src/sage/combinat/root_system/cartan_matrix.py
+++ b/src/sage/combinat/root_system/cartan_matrix.py
@@ -32,7 +32,7 @@
 from sage.matrix.matrix_space import MatrixSpace
 from sage.misc.inherit_comparison import InheritComparisonClasscallMetaclass
 from sage.misc.classcall_metaclass import typecall
-from sage.misc.misc import powerset
+from sage.combinat.subset import powerset
 from sage.matrix.matrix_integer_sparse import Matrix_integer_sparse
 from sage.rings.integer_ring import ZZ
 from sage.combinat.root_system.cartan_type import CartanType, CartanType_abstract
diff --git a/src/sage/combinat/root_system/coxeter_type.py b/src/sage/combinat/root_system/coxeter_type.py
index 39fa6ca0d01..cad3482bb17 100644
--- a/src/sage/combinat/root_system/coxeter_type.py
+++ b/src/sage/combinat/root_system/coxeter_type.py
@@ -17,17 +17,20 @@
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
+import sage.rings.abc
+
+from sage.combinat.root_system.cartan_type import CartanType
 from sage.misc.abstract_method import abstract_method
 from sage.misc.cachefunc import cached_method
 from sage.misc.classcall_metaclass import ClasscallMetaclass
-from sage.combinat.root_system.cartan_type import CartanType
-import sage.rings.abc
 from sage.matrix.args import SparseEntry
 from sage.matrix.constructor import Matrix
-from sage.symbolic.ring import SR
+from sage.misc.lazy_import import lazy_import
 from sage.structure.unique_representation import UniqueRepresentation
 from sage.structure.sage_object import SageObject
 
+lazy_import('sage.rings.universal_cyclotomic_field', 'UniversalCyclotomicField')
+
 
 class CoxeterType(SageObject, metaclass=ClasscallMetaclass):
     """
@@ -372,19 +375,12 @@ def bilinear_form(self, R=None):
         n = self.rank()
         mat = self.coxeter_matrix()._matrix
 
-        from sage.rings.universal_cyclotomic_field import UniversalCyclotomicField
-        UCF = UniversalCyclotomicField()
-
         if R is None:
-            R = UCF
-        # if UCF.has_coerce_map_from(base_ring):
-        #     R = UCF
-        # else:
-        #     R = base_ring
+            R = UniversalCyclotomicField()
 
         # Compute the matrix with entries `- \cos( \pi / m_{ij} )`.
-        E = UCF.gen
-        if R is UCF:
+        if isinstance(R, sage.rings.abc.UniversalCyclotomicField):
+            E = R.gen
 
             def val(x):
                 if x > -1:
@@ -392,6 +388,7 @@ def val(x):
                 else:
                     return R(x)
         elif isinstance(R, sage.rings.abc.NumberField_quadratic):
+            E = UniversalCyclotomicField().gen
 
             def val(x):
                 if x > -1:
@@ -401,6 +398,7 @@ def val(x):
         else:
             from sage.functions.trig import cos
             from sage.symbolic.constants import pi
+            from sage.symbolic.ring import SR
 
             def val(x):
                 if x > -1:
diff --git a/src/sage/combinat/set_partition.py b/src/sage/combinat/set_partition.py
index 6edf7d963da..3c3acef4299 100644
--- a/src/sage/combinat/set_partition.py
+++ b/src/sage/combinat/set_partition.py
@@ -40,6 +40,7 @@
 from sage.categories.infinite_enumerated_sets import InfiniteEnumeratedSets
 from sage.categories.finite_enumerated_sets import FiniteEnumeratedSets
 from sage.misc.inherit_comparison import InheritComparisonClasscallMetaclass
+from sage.misc.lazy_import import lazy_import
 from sage.rings.infinity import infinity
 from sage.rings.integer import Integer
 from sage.combinat.combinatorial_map import combinatorial_map
@@ -50,9 +51,10 @@
 from sage.combinat.permutation import Permutation
 from sage.arith.misc import factorial
 from sage.misc.prandom import random, randint, sample
-from sage.probability.probability_distribution import GeneralDiscreteDistribution
 from sage.sets.disjoint_set import DisjointSet
-from sage.combinat.posets.hasse_diagram import HasseDiagram
+
+lazy_import('sage.combinat.posets.hasse_diagram', 'HasseDiagram')
+lazy_import('sage.probability.probability_distribution', 'GeneralDiscreteDistribution')
 
 
 class AbstractSetPartition(ClonableArray,
diff --git a/src/sage/combinat/subset.py b/src/sage/combinat/subset.py
index c27b1eb04ed..a08a5474cae 100644
--- a/src/sage/combinat/subset.py
+++ b/src/sage/combinat/subset.py
@@ -39,7 +39,6 @@
 
 from sage.sets.set import Set, Set_object_enumerated
 from sage.arith.misc import binomial
-from sage.misc.misc import _stable_uniq as uniq
 from sage.rings.integer_ring import ZZ
 from sage.rings.integer import Integer
 from . import combination
@@ -1471,3 +1470,93 @@ def _element_constructor_(self, x):
             [(), (0,), (1,), (2,), (0, 1), (0, 2), (1, 2), (0, 1, 2)]
         """
         return self.element_class(sorted(set(x)))
+
+
+def powerset(X):
+    r"""
+    Iterator over the *list* of all subsets of the iterable ``X``, in no
+    particular order. Each list appears exactly once, up to order.
+
+    INPUT:
+
+    -  ``X`` - an iterable
+
+    OUTPUT: iterator of lists
+
+    EXAMPLES::
+
+        sage: list(powerset([1,2,3]))
+        [[], [1], [2], [1, 2], [3], [1, 3], [2, 3], [1, 2, 3]]
+        sage: [z for z in powerset([0,[1,2]])]
+        [[], [0], [[1, 2]], [0, [1, 2]]]
+
+    Iterating over the power set of an infinite set is also allowed::
+
+        sage: i = 0
+        sage: L = []
+        sage: for x in powerset(ZZ):
+        ....:     if i > 10:
+        ....:         break
+        ....:     else:
+        ....:         i += 1
+        ....:     L.append(x)
+        sage: print(" ".join(str(x) for x in L))
+        [] [0] [1] [0, 1] [-1] [0, -1] [1, -1] [0, 1, -1] [2] [0, 2] [1, 2]
+
+    You may also use subsets as an alias for powerset::
+
+        sage: subsets([1,2,3])
+        <generator object ...powerset at 0x...>
+        sage: list(subsets([1,2,3]))
+        [[], [1], [2], [1, 2], [3], [1, 3], [2, 3], [1, 2, 3]]
+
+        The reason we return lists instead of sets is that the elements of
+        sets must be hashable and many structures on which one wants the
+        powerset consist of non-hashable objects.
+
+    AUTHORS:
+
+    - William Stein
+
+    - Nils Bruin (2006-12-19): rewrite to work for not-necessarily
+      finite objects X.
+    """
+    yield []
+    pairs = []
+    power2 = 1
+    for x in X:
+        pairs.append((power2, x))
+        next_power2 = power2 << 1
+        for w in range(power2, next_power2):
+            yield [x for m, x in pairs if m & w]
+        power2 = next_power2
+
+
+subsets = powerset
+
+
+def uniq(L):
+    """
+    Iterate over the elements of ``L``, yielding every element at most
+    once: keep only the first occurrence of any item.
+
+    The items must be hashable.
+
+    INPUT:
+
+    - ``L`` -- iterable
+
+    EXAMPLES::
+
+        sage: L = [1, 1, 8, -5, 3, -5, 'a', 'x', 'a']
+        sage: it = uniq(L); it
+        <generator object uniq at ...>
+        sage: list(it)
+        [1, 8, -5, 3, 'a', 'x']
+    """
+    seen = set()
+    for x in L:
+        if x in seen:
+            continue
+        yield x
+        seen.add(x)
diff --git a/src/sage/combinat/tableau.py b/src/sage/combinat/tableau.py
index 4df26efd41d..c33a09fd483 100644
--- a/src/sage/combinat/tableau.py
+++ b/src/sage/combinat/tableau.py
@@ -100,7 +100,7 @@
 from sage.combinat.posets.posets import Poset
 from sage.groups.perm_gps.permgroup import PermutationGroup
 from sage.misc.inherit_comparison import InheritComparisonClasscallMetaclass
-from sage.misc.misc import powerset
+from sage.combinat.subset import powerset
 from sage.misc.misc_c import prod
 from sage.misc.persist import register_unpickle_override
 from sage.rings.finite_rings.integer_mod_ring import IntegerModRing
diff --git a/src/sage/databases/jones.py b/src/sage/databases/jones.py
index 6f6318d0c2d..5afcaaa3f6b 100644
--- a/src/sage/databases/jones.py
+++ b/src/sage/databases/jones.py
@@ -71,7 +71,7 @@
 from sage.rings.number_field.number_field import NumberField
 from sage.rings.rational_field import RationalField
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-from sage.misc.misc import powerset
+from sage.combinat.subset import powerset
 from sage.env import SAGE_SHARE
 
 from sage.misc.persist import load, save
diff --git a/src/sage/dynamics/arithmetic_dynamics/projective_ds_helper.pyx b/src/sage/dynamics/arithmetic_dynamics/projective_ds_helper.pyx
index dcb12407b7a..3d40d748a17 100644
--- a/src/sage/dynamics/arithmetic_dynamics/projective_ds_helper.pyx
+++ b/src/sage/dynamics/arithmetic_dynamics/projective_ds_helper.pyx
@@ -21,7 +21,7 @@ AUTHORS:
 
 from sage.arith.functions cimport LCM_list
 from sage.rings.finite_rings.finite_field_constructor import GF
-from sage.misc.misc import subsets
+from sage.combinat.subset import subsets
 
 
 cpdef _fast_possible_periods(self, return_points=False):
diff --git a/src/sage/game_theory/cooperative_game.py b/src/sage/game_theory/cooperative_game.py
index 0cb18189191..b95ba0f655a 100644
--- a/src/sage/game_theory/cooperative_game.py
+++ b/src/sage/game_theory/cooperative_game.py
@@ -21,7 +21,7 @@
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
 from itertools import permutations, combinations
-from sage.misc.misc import powerset
+from sage.combinat.subset import powerset
 from sage.rings.integer import Integer
 from sage.structure.sage_object import SageObject
 
diff --git a/src/sage/game_theory/normal_form_game.py b/src/sage/game_theory/normal_form_game.py
index 5068c8e10e3..cd6e371eeb2 100644
--- a/src/sage/game_theory/normal_form_game.py
+++ b/src/sage/game_theory/normal_form_game.py
@@ -635,7 +635,7 @@
 from itertools import product
 from .parser import Parser
 from sage.misc.latex import latex
-from sage.misc.misc import powerset
+from sage.combinat.subset import powerset
 from sage.rings.rational_field import QQ
 from sage.structure.sage_object import SageObject
 from sage.matrix.constructor import matrix
diff --git a/src/sage/geometry/polyhedral_complex.py b/src/sage/geometry/polyhedral_complex.py
index 629a4f9ba2a..cff7b73c94e 100644
--- a/src/sage/geometry/polyhedral_complex.py
+++ b/src/sage/geometry/polyhedral_complex.py
@@ -117,7 +117,7 @@
 from sage.rings.integer_ring import ZZ
 from sage.graphs.graph import Graph
 from sage.combinat.posets.posets import Poset
-from sage.misc.misc import powerset
+from sage.combinat.subset import powerset
 
 
 class PolyhedralComplex(GenericCellComplex):
diff --git a/src/sage/graphs/graph.py b/src/sage/graphs/graph.py
index b351b8501c0..8aa4efbce0f 100644
--- a/src/sage/graphs/graph.py
+++ b/src/sage/graphs/graph.py
@@ -3946,7 +3946,7 @@ def chromatic_symmetric_function(self, R=None):
         """
         from sage.combinat.sf.sf import SymmetricFunctions
         from sage.combinat.partition import _Partitions
-        from sage.misc.misc import powerset
+        from sage.combinat.subset import powerset
         if R is None:
             R = ZZ
         p = SymmetricFunctions(R).p()
diff --git a/src/sage/misc/all.py b/src/sage/misc/all.py
index 8fea19524eb..b58c90e5c22 100644
--- a/src/sage/misc/all.py
+++ b/src/sage/misc/all.py
@@ -7,7 +7,6 @@
 
 from .misc import (BackslashOperator,
                   cputime,
-                  union, uniq, powerset, subsets,
                   exists, forall, is_iterator,
                   random_sublist, walltime,
                   pad_zeros,
diff --git a/src/sage/misc/misc.py b/src/sage/misc/misc.py
index f263f53bad3..ac285817431 100644
--- a/src/sage/misc/misc.py
+++ b/src/sage/misc/misc.py
@@ -48,6 +48,9 @@
 from sage.env import DOT_SAGE, HOSTNAME
 from sage.misc.lazy_import import lazy_import
 
+lazy_import("sage.combinat.subset", ["powerset", "subsets", "uniq"],
+            deprecation=35564)
+
 lazy_import("sage.misc.call", ["AttrCallObject", "attrcall", "call_method"],
             deprecation=29869)
 
@@ -554,53 +557,6 @@ def union(x, y=None):
     return list(set(x).union(y))
 
 
-def uniq(x):
-    """
-    Return the sublist of all elements in the list x that is sorted and
-    is such that the entries in the sublist are unique.
-
-    EXAMPLES::
-
-        sage: uniq([1, 1, 8, -5, 3, -5, -13, 13, -13])
-        doctest:...: DeprecationWarning: the output of uniq(X) being sorted is deprecated; use sorted(set(X)) instead if you want sorted output
-        See https://github.com/sagemath/sage/issues/27014 for details.
-        [-13, -5, 1, 3, 8, 13]
-    """
-    # After deprecation period, rename _stable_uniq -> uniq
-    from sage.misc.superseded import deprecation
-    deprecation(27014, "the output of uniq(X) being sorted is deprecated; use sorted(set(X)) instead if you want sorted output")
-    return sorted(set(x))
-
-
-def _stable_uniq(L):
-    """
-    Iterate over the elements of ``L``, yielding every element at most
-    once: keep only the first occurrence of any item.
-
-    The items must be hashable.
-
-    INPUT:
-
-    - ``L`` -- iterable
-
-    EXAMPLES::
-
-        sage: from sage.misc.misc import _stable_uniq
-        sage: L = [1, 1, 8, -5, 3, -5, 'a', 'x', 'a']
-        sage: it = _stable_uniq(L)
-        sage: it
-        <generator object _stable_uniq at ...>
-        sage: list(it)
-        [1, 8, -5, 3, 'a', 'x']
-    """
-    seen = set()
-    for x in L:
-        if x in seen:
-            continue
-        yield x
-        seen.add(x)
-
-
 def exactly_one_is_true(iterable):
     r"""
     Return whether exactly one element of ``iterable`` evaluates ``True``.
@@ -1056,69 +1012,6 @@ def _some_tuples_sampling(elements, repeat, max_samples, n):
             yield tuple(elements[j] for j in Integer(a).digits(n, padto=repeat))
 
 
-def powerset(X):
-    r"""
-    Iterator over the *list* of all subsets of the iterable X, in no
-    particular order. Each list appears exactly once, up to order.
-
-    INPUT:
-
-    -  ``X`` - an iterable
-
-    OUTPUT: iterator of lists
-
-    EXAMPLES::
-
-        sage: list(powerset([1,2,3]))
-        [[], [1], [2], [1, 2], [3], [1, 3], [2, 3], [1, 2, 3]]
-        sage: [z for z in powerset([0,[1,2]])]
-        [[], [0], [[1, 2]], [0, [1, 2]]]
-
-    Iterating over the power set of an infinite set is also allowed::
-
-        sage: i = 0
-        sage: L = []
-        sage: for x in powerset(ZZ):
-        ....:     if i > 10:
-        ....:         break
-        ....:     else:
-        ....:         i += 1
-        ....:     L.append(x)
-        sage: print(" ".join(str(x) for x in L))
-        [] [0] [1] [0, 1] [-1] [0, -1] [1, -1] [0, 1, -1] [2] [0, 2] [1, 2]
-
-    You may also use subsets as an alias for powerset::
-
-        sage: subsets([1,2,3])
-        <generator object ...powerset at 0x...>
-        sage: list(subsets([1,2,3]))
-        [[], [1], [2], [1, 2], [3], [1, 3], [2, 3], [1, 2, 3]]
-
-        The reason we return lists instead of sets is that the elements of
-        sets must be hashable and many structures on which one wants the
-        powerset consist of non-hashable objects.
-
-    AUTHORS:
-
-    - William Stein
-
-    - Nils Bruin (2006-12-19): rewrite to work for not-necessarily
-      finite objects X.
-    """
-    yield []
-    pairs = []
-    power2 = 1
-    for x in X:
-        pairs.append((power2, x))
-        next_power2 = power2 << 1
-        for w in range(power2, next_power2):
-            yield [x for m, x in pairs if m & w]
-        power2 = next_power2
-
-
-subsets = powerset
-
-
 #################################################################
 # Misc.
 #################################################################
diff --git a/src/sage/rings/abc.pyx b/src/sage/rings/abc.pyx
index 2aa3421721d..d967cfbb95c 100644
--- a/src/sage/rings/abc.pyx
+++ b/src/sage/rings/abc.pyx
@@ -56,6 +56,32 @@ class NumberField_cyclotomic(Field):
     pass
 
 
+class UniversalCyclotomicField(Field):
+    r"""
+    Abstract base class for :class:`~sage.rings.universal_cyclotomic_field.UniversalCyclotomicField`.
+
+    This class is defined for the purpose of :func:`isinstance` tests.  It should not be
+    instantiated.
+
+    EXAMPLES::
+
+        sage: import sage.rings.abc
+        sage: K = UniversalCyclotomicField()                                            # optional - sage.rings.number_field
+        sage: isinstance(K, sage.rings.abc.UniversalCyclotomicField)                    # optional - sage.rings.number_field
+        True
+
+    By design, there is a unique direct subclass::
+
+        sage: sage.rings.abc.UniversalCyclotomicField.__subclasses__()                  # optional - sage.rings.number_field
+        [<class 'sage.rings.universal_cyclotomic_field.UniversalCyclotomicField'>]
+
+        sage: len(sage.rings.abc.NumberField_cyclotomic.__subclasses__()) <= 1
+        True
+    """
+
+    pass
+
+
 class AlgebraicField_common(Field):
     r"""
     Abstract base class for :class:`~sage.rings.qqbar.AlgebraicField_common`.
diff --git a/src/sage/rings/function_field/ideal.py b/src/sage/rings/function_field/ideal.py
index 8d203e9f019..25317e4d80c 100644
--- a/src/sage/rings/function_field/ideal.py
+++ b/src/sage/rings/function_field/ideal.py
@@ -93,7 +93,7 @@
 # ****************************************************************************
 
 from sage.misc.latex import latex
-from sage.misc.misc import powerset
+from sage.combinat.subset import powerset
 from sage.structure.parent import Parent
 from sage.structure.element import Element
 from sage.structure.richcmp import richcmp
diff --git a/src/sage/rings/polynomial/cyclotomic.pyx b/src/sage/rings/polynomial/cyclotomic.pyx
index c4594dba8ad..ed0558413ea 100644
--- a/src/sage/rings/polynomial/cyclotomic.pyx
+++ b/src/sage/rings/polynomial/cyclotomic.pyx
@@ -35,7 +35,7 @@ from sage.structure.element cimport parent
 from sage.arith.misc import factor
 from sage.rings.integer_ring import ZZ
 from sage.misc.misc_c import prod
-from sage.misc.misc import subsets
+from sage.combinat.subset import subsets
 from sage.libs.pari.all import pari
 
 
diff --git a/src/sage/rings/universal_cyclotomic_field.py b/src/sage/rings/universal_cyclotomic_field.py
index 2c6097e74e8..173224323ce 100644
--- a/src/sage/rings/universal_cyclotomic_field.py
+++ b/src/sage/rings/universal_cyclotomic_field.py
@@ -163,6 +163,8 @@
 - Sebastian Oehms (2019): add :meth:`_factor_univariate_polynomial` (see :trac:`28631`)
 """
 
+import sage.rings.abc
+
 from sage.misc.cachefunc import cached_method
 
 from sage.structure.richcmp import rich_to_bool
@@ -1281,7 +1283,7 @@ def minpoly(self, var='x'):
         return QQ[var](QQ['x_1'](str(gap_p)))
 
 
-class UniversalCyclotomicField(UniqueRepresentation, Field):
+class UniversalCyclotomicField(UniqueRepresentation, sage.rings.abc.UniversalCyclotomicField):
     r"""
     The universal cyclotomic field.
 
diff --git a/src/sage/sets/condition_set.py b/src/sage/sets/condition_set.py
index 34265775dd3..de33e6f655e 100644
--- a/src/sage/sets/condition_set.py
+++ b/src/sage/sets/condition_set.py
@@ -18,7 +18,7 @@
 from sage.categories.sets_cat import Sets
 from sage.categories.enumerated_sets import EnumeratedSets
 from sage.misc.cachefunc import cached_method
-from sage.misc.misc import _stable_uniq
+from sage.combinat.subset import uniq
 from sage.structure.element import Expression
 from .set import Set, Set_base, Set_boolean_operators, Set_add_sub_operators
 
@@ -173,7 +173,7 @@ def __classcall_private__(cls, universe, *predicates, vars=None, names=None, cat
             else:
                 other_predicates.append(predicate)
 
-        predicates = list(_stable_uniq(callable_symbolic_predicates + other_predicates))
+        predicates = list(uniq(callable_symbolic_predicates + other_predicates))
 
         if not other_predicates and not callable_symbolic_predicates:
             if names is None and category is None: