diff --git a/seaborn/_core/mappings.py b/seaborn/_core/mappings.py
index 97ad03adbf..d23eb7ae54 100644
--- a/seaborn/_core/mappings.py
+++ b/seaborn/_core/mappings.py
@@ -16,6 +16,7 @@
 from typing import TYPE_CHECKING
 if TYPE_CHECKING:
     from typing import Any, Callable, Optional, Tuple
+    from numpy.typing import ArrayLike
     from pandas import Series
     from matplotlib.colors import Colormap
     from matplotlib.scale import Scale
@@ -27,20 +28,32 @@
 
 class IdentityTransform:
 
-    def __call__(self, x):
+    def __call__(self, x: Any) -> Any:
         return x
 
 
 class RangeTransform:
 
-    def __init__(self, lo: float, hi: float):
-        self.out_range = lo, hi
+    def __init__(self, out_range: tuple[float, float]):
+        self.out_range = out_range
 
-    def __call__(self, x: float) -> float:
+    def __call__(self, x: ArrayLike) -> ArrayLike:
         lo, hi = self.out_range
         return lo + x * (hi - lo)
 
-# TODO RGBTransform?
+
+class RGBTransform:
+
+    def __init__(self, cmap: Colormap):
+        self.cmap = cmap
+
+    def __call__(self, x: ArrayLike) -> ArrayLike:
+        # TODO should implement a general vectorized to_rgb(a)
+        rgba = self.cmap(x)
+        if isinstance(rgba, tuple):
+            return to_rgb(rgba)
+        else:
+            return rgba[..., :3]
 
 
 # ==================================================================================== #
@@ -167,7 +180,7 @@ def _infer_map_type(
         if scale is not None:
             return scale.type
         elif isinstance(values, (list, dict)):
-            return "categorical"
+            return VarType("categorical")
         else:
             map_type = variable_type(data, boolean_type="categorical")
         return map_type
@@ -192,7 +205,10 @@ def setup(
 
         if map_type == "numeric":
 
-            transform = RangeTransform(*values)
+            if not isinstance(values, tuple):
+                raise TypeError()  # TODO
+
+            transform = RangeTransform(values)
 
             if not norm.scaled():
                 # Initialize auto-limits
@@ -205,9 +221,8 @@ def setup(
             if isinstance(values, tuple):
                 # TODO even spacing between these values, large to small?
                 numbers = np.linspace(1, 0, len(levels))
-                transform = RangeTransform(*values)
-                values = transform(numbers)
-                mapping_dict = dict(zip(levels, values))
+                transform = RangeTransform(values)
+                mapping_dict = dict(zip(levels, transform(numbers)))
             elif isinstance(values, dict):
                 self._check_dict_not_missing_levels(levels, values)
                 mapping_dict = values
@@ -348,15 +363,9 @@ def _setup_numeric(
             norm.autoscale_None(data.dropna())
             mapping = {}
 
-        def rgb_transform(x):
-            rgba = cmap(x)
-            # TODO we should have general vectorized to_rgb/to_rgba
-            if isinstance(rgba, tuple):
-                return to_rgb(rgba)
-            else:
-                return rgba[..., :3]
+        transform = RGBTransform(cmap)
 
-        return mapping, norm, rgb_transform
+        return mapping, norm, transform
 
     def _infer_map_type(
         self,