diff --git a/src/sage/topology/simplicial_complex_homset.py b/src/sage/topology/simplicial_complex_homset.py
index 7b9aceb8b64..40b17a3c524 100644
--- a/src/sage/topology/simplicial_complex_homset.py
+++ b/src/sage/topology/simplicial_complex_homset.py
@@ -61,32 +61,6 @@
 from .simplicial_complex_morphism import SimplicialComplexMorphism
 
 
-def is_SimplicialComplexHomset(x) -> bool:
-    """
-    Return ``True`` if and only if ``x`` is a simplicial complex homspace.
-
-    EXAMPLES::
-
-        sage: S = SimplicialComplex(is_mutable=False)
-        sage: T = SimplicialComplex(is_mutable=False)
-        sage: H = Hom(S, T)
-        sage: H
-        Set of Morphisms from Simplicial complex with vertex set () and facets {()}
-         to Simplicial complex with vertex set () and facets {()}
-         in Category of finite simplicial complexes
-        sage: from sage.topology.simplicial_complex_homset import is_SimplicialComplexHomset
-        sage: is_SimplicialComplexHomset(H)
-        doctest:warning...
-        DeprecationWarning: the function is_SimplicialComplexHomset is deprecated;
-        use 'isinstance(..., SimplicialComplexHomset)' instead
-        See https://github.com/sagemath/sage/issues/37922 for details.
-        True
-    """
-    from sage.misc.superseded import deprecation
-    deprecation(37922, "the function is_SimplicialComplexHomset is deprecated; use 'isinstance(..., SimplicialComplexHomset)' instead")
-    return isinstance(x, SimplicialComplexHomset)
-
-
 class SimplicialComplexHomset(sage.categories.homset.Homset):
     def __call__(self, f):
         """
diff --git a/src/sage/topology/simplicial_complex_morphism.py b/src/sage/topology/simplicial_complex_morphism.py
index 044f794769b..cbaa6e167a4 100644
--- a/src/sage/topology/simplicial_complex_morphism.py
+++ b/src/sage/topology/simplicial_complex_morphism.py
@@ -114,36 +114,11 @@
 lazy_import('sage.matrix.constructor', ['matrix', 'zero_matrix'])
 
 
-def is_SimplicialComplexMorphism(x):
-    """
-    Return ``True`` if and only if ``x`` is a morphism of simplicial complexes.
-
-    EXAMPLES::
-
-        sage: from sage.topology.simplicial_complex_morphism import is_SimplicialComplexMorphism
-        sage: S = SimplicialComplex([[0,1],[3,4]], is_mutable=False)
-        sage: H = Hom(S,S)
-        sage: f = {0:0,1:1,3:3,4:4}
-        sage: x = H(f)
-        sage: is_SimplicialComplexMorphism(x)
-        doctest:warning...
-        DeprecationWarning: The function is_SimplicialComplexMorphism is deprecated;
-        use 'isinstance(..., SimplicialComplexMorphism)' instead.
-        See https://github.com/sagemath/sage/issues/38103 for details.
-        True
-    """
-    from sage.misc.superseded import deprecation
-    deprecation(38103,
-                "The function is_SimplicialComplexMorphism is deprecated; "
-                "use 'isinstance(..., SimplicialComplexMorphism)' instead.")
-    return isinstance(x, SimplicialComplexMorphism)
-
-
 class SimplicialComplexMorphism(Morphism):
     """
     An element of this class is a morphism of simplicial complexes.
     """
-    def __init__(self, f, X, Y):
+    def __init__(self, f, X, Y) -> None:
         """
         Input is a dictionary ``f``, the domain ``X``, and the codomain ``Y``.
 
@@ -181,7 +156,7 @@ def __init__(self, f, X, Y):
         self._vertex_dictionary = f
         Morphism.__init__(self, Hom(X, Y, SimplicialComplexes()))
 
-    def __eq__(self, x):
+    def __eq__(self, x) -> bool:
         """
         Return ``True`` if and only if ``self == x``.
 
@@ -291,7 +266,7 @@ def __call__(self, x, orientation=False):
         else:
             return Simplex(set(fx))
 
-    def _repr_type(self):
+    def _repr_type(self) -> str:
         """
         EXAMPLES::
 
@@ -304,7 +279,7 @@ def _repr_type(self):
         """
         return "Simplicial complex"
 
-    def _repr_defn(self):
+    def _repr_defn(self) -> str:
         """
         If there are fewer than 5 vertices, print the image of each vertex
         on a separate line. Otherwise, print the map as a single line.
@@ -502,7 +477,7 @@ def image(self):
         fa = [self(i) for i in self.domain().facets()]
         return SimplicialComplex(fa, maximality_check=True)
 
-    def is_surjective(self):
+    def is_surjective(self) -> bool:
         """
         Return ``True`` if and only if ``self`` is surjective.
 
@@ -529,7 +504,7 @@ def is_surjective(self):
         """
         return self.codomain() == self.image()
 
-    def is_injective(self):
+    def is_injective(self) -> bool:
         """
         Return ``True`` if and only if ``self`` is injective.
 
@@ -550,7 +525,7 @@ def is_injective(self):
             True
         """
         v = [self._vertex_dictionary[i[0]] for i in self.domain().faces()[0]]
-        return all(v.count(i) <= 1 for i in v)
+        return len(v) == len(set(v))
 
     def is_identity(self) -> bool:
         """