diff --git a/src/sage/categories/functor.pyx b/src/sage/categories/functor.pyx
index f548adfc664..08b0d966f2b 100644
--- a/src/sage/categories/functor.pyx
+++ b/src/sage/categories/functor.pyx
@@ -385,8 +385,8 @@ cdef class Functor(SageObject):
             that is not in Category of rings.
 
         """
-        from sage.categories.morphism import is_Morphism
-        if is_Morphism(x):
+        from sage.categories.morphism import Morphism
+        if isinstance(x, Morphism):
             return self._apply_functor_to_morphism(x)
         y = self._apply_functor(self._coerce_into_domain(x))
         if not ((y in self.__codomain) or (y in self.__codomain.Homsets())):
diff --git a/src/sage/categories/map.pyx b/src/sage/categories/map.pyx
index 134b88ef1ba..67331807ec1 100644
--- a/src/sage/categories/map.pyx
+++ b/src/sage/categories/map.pyx
@@ -62,8 +62,13 @@ def is_Map(x):
         sage: f = R.hom([x+y, x-y], R)
         sage: from sage.categories.map import is_Map
         sage: is_Map(f)
+        doctest:warning...
+        DeprecationWarning: The function is_Map is deprecated; use 'isinstance(..., Map)' instead.
+        See https://github.com/sagemath/sage/issues/38103 for details.
         True
     """
+    from sage.misc.superseded import deprecation_cython
+    deprecation_cython(38103, "The function is_Map is deprecated; use 'isinstance(..., Map)' instead.")
     return isinstance(x, Map)
 
 
diff --git a/src/sage/categories/morphism.pyx b/src/sage/categories/morphism.pyx
index 57e00943eda..3666492a794 100644
--- a/src/sage/categories/morphism.pyx
+++ b/src/sage/categories/morphism.pyx
@@ -47,6 +47,8 @@ from sage.structure.parent cimport Parent
 
 
 def is_Morphism(x):
+    from sage.misc.superseded import deprecation_cython
+    deprecation_cython(38103, "The function is_Morphism is deprecated; use 'isinstance(..., Morphism)' instead.")
     return isinstance(x, Morphism)
 
 
diff --git a/src/sage/groups/abelian_gps/abelian_group_morphism.py b/src/sage/groups/abelian_gps/abelian_group_morphism.py
index a44abb83df9..eb41400065a 100644
--- a/src/sage/groups/abelian_gps/abelian_group_morphism.py
+++ b/src/sage/groups/abelian_gps/abelian_group_morphism.py
@@ -25,6 +25,10 @@
 
 
 def is_AbelianGroupMorphism(f):
+    from sage.misc.superseded import deprecation
+    deprecation(38103,
+                "The function is_AbelianGroupMorphism is deprecated; "
+                "use 'isinstance(..., AbelianGroupMorphism)' instead.")
     return isinstance(f, AbelianGroupMorphism)
 
 
diff --git a/src/sage/groups/perm_gps/permgroup_morphism.py b/src/sage/groups/perm_gps/permgroup_morphism.py
index 206828b4e1a..c0596d94b85 100644
--- a/src/sage/groups/perm_gps/permgroup_morphism.py
+++ b/src/sage/groups/perm_gps/permgroup_morphism.py
@@ -321,6 +321,14 @@ def is_PermutationGroupMorphism(f) -> bool:
         sage: H = DihedralGroup(4)
         sage: phi = PermutationGroupMorphism_im_gens(G, H, map(H, G.gens()))
         sage: is_PermutationGroupMorphism(phi)
+        doctest:warning...
+        DeprecationWarning: The function is_PermutationGroupMorphism is deprecated;
+        use 'isinstance(..., PermutationGroupMorphism)' instead.
+        See https://github.com/sagemath/sage/issues/38103 for details.
         True
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38103,
+                "The function is_PermutationGroupMorphism is deprecated; "
+                "use 'isinstance(..., PermutationGroupMorphism)' instead.")
     return isinstance(f, PermutationGroupMorphism)
diff --git a/src/sage/homology/chain_complex_morphism.py b/src/sage/homology/chain_complex_morphism.py
index e1bddf920e4..af68bf0c906 100644
--- a/src/sage/homology/chain_complex_morphism.py
+++ b/src/sage/homology/chain_complex_morphism.py
@@ -78,8 +78,16 @@ def is_ChainComplexMorphism(x):
           From: Chain complex with at most 7 nonzero terms over Integer Ring
           To: Chain complex with at most 7 nonzero terms over Integer Ring
         sage: is_ChainComplexMorphism(x)
+        doctest:warning...
+        DeprecationWarning: The function is_ChainComplexMorphism is deprecated;
+        use 'isinstance(..., ChainComplexMorphism)' instead.
+        See https://github.com/sagemath/sage/issues/38103 for details.
         True
     """
+    from sage.misc.superseded import deprecation
+    deprecation(38103,
+                "The function is_ChainComplexMorphism is deprecated; "
+                "use 'isinstance(..., ChainComplexMorphism)' instead.")
     return isinstance(x, ChainComplexMorphism)
 
 
diff --git a/src/sage/modules/fg_pid/fgp_morphism.py b/src/sage/modules/fg_pid/fgp_morphism.py
index ae8309d6d87..4be28f43be1 100644
--- a/src/sage/modules/fg_pid/fgp_morphism.py
+++ b/src/sage/modules/fg_pid/fgp_morphism.py
@@ -20,7 +20,7 @@
 #                  https://www.gnu.org/licenses/
 # *************************************************************************
 
-from sage.categories.morphism import Morphism, is_Morphism
+from sage.categories.morphism import Morphism
 from .fgp_module import DEBUG
 from sage.structure.richcmp import richcmp, op_NE
 from sage.misc.cachefunc import cached_method
@@ -101,7 +101,7 @@ def __init__(self, parent, phi, check=True):
         # input: phi is a morphism from MO = M.optimized().V() to N.V()
         # that sends MO.W() to N.W()
         if check:
-            if not is_Morphism(phi) and M == N:
+            if not isinstance(phi, Morphism) and M == N:
                 A = M.optimized()[0].V()
                 B = N.V()
                 s = M.base_ring()(phi) * B.coordinate_module(A).basis_matrix()
diff --git a/src/sage/quivers/morphism.py b/src/sage/quivers/morphism.py
index a1afbe79d1c..f6c2ca180a6 100644
--- a/src/sage/quivers/morphism.py
+++ b/src/sage/quivers/morphism.py
@@ -267,11 +267,11 @@ def __init__(self, domain, codomain, data={}):
                 start_index += dim
 
         # Get the coordinates of the vector
-        from sage.categories.map import is_Map
+        from sage.categories.map import Map
         vector = []
         for v in self._quiver:
             if v in maps_dict:
-                if is_Map(maps_dict[v]):
+                if isinstance(maps_dict[v], Map):
                     try:
                         m = maps_dict[v].matrix()
                     except (AttributeError, ValueError):
diff --git a/src/sage/quivers/representation.py b/src/sage/quivers/representation.py
index 0d5aa2aa396..be58c37fd70 100644
--- a/src/sage/quivers/representation.py
+++ b/src/sage/quivers/representation.py
@@ -710,7 +710,7 @@ def create_key(self, k, P, *args, **kwds):
             # Note that the first space is assigned to key[3] and the first
             # vertex is 1 so the space assigned to vertex v is key[2 + v]
             from sage.matrix.constructor import Matrix
-            from sage.categories.morphism import is_Morphism
+            from sage.categories.morphism import Morphism
             for x in P._sorted_edges:
                 if x in maps:
                     e = maps[x]
@@ -724,7 +724,7 @@ def create_key(self, k, P, *args, **kwds):
                 # If a morphism is specified take it's matrix.  Create one if
                 # needed.  Otherwise assume the Matrix function can convert the
                 # object to a Matrix.
-                if is_Morphism(e):
+                if isinstance(e, Morphism):
                     if hasattr(e, 'matrix'):
                         key.append(e.matrix())
                     else:
diff --git a/src/sage/rings/finite_rings/finite_field_base.pyx b/src/sage/rings/finite_rings/finite_field_base.pyx
index 2c49f3bc9ae..661b2ba08e6 100644
--- a/src/sage/rings/finite_rings/finite_field_base.pyx
+++ b/src/sage/rings/finite_rings/finite_field_base.pyx
@@ -1260,7 +1260,7 @@ cdef class FiniteField(Field):
             return self.__vector_space
 
         from sage.modules.free_module import VectorSpace
-        from sage.categories.morphism import is_Morphism
+        from sage.categories.morphism import Morphism
 
         if base is None:
             base = self.prime_subfield()
@@ -1269,7 +1269,7 @@ cdef class FiniteField(Field):
                 self.__vector_space = VectorSpace(base, s)
             V = self.__vector_space
             inclusion_map = None
-        elif is_Morphism(base):
+        elif isinstance(base, Morphism):
             inclusion_map = base
             base = inclusion_map.domain()
             s = self.degree() // base.degree()
diff --git a/src/sage/rings/ideal.py b/src/sage/rings/ideal.py
index e4b41b438a5..96bd7d71380 100644
--- a/src/sage/rings/ideal.py
+++ b/src/sage/rings/ideal.py
@@ -539,8 +539,8 @@ def apply_morphism(self, phi):
             sage: taus[1](B)                                                            # needs sage.rings.number_fields
             Fractional ideal (2, a + 1)
         """
-        from sage.categories.morphism import is_Morphism
-        if not is_Morphism(phi):
+        from sage.categories.morphism import Morphism
+        if not isinstance(phi, Morphism):
             raise TypeError("phi must be a morphism")
         # delegate: morphisms know how to apply themselves to ideals
         return phi(self)
diff --git a/src/sage/rings/number_field/number_field.py b/src/sage/rings/number_field/number_field.py
index e13806ad619..5787b1196b2 100644
--- a/src/sage/rings/number_field/number_field.py
+++ b/src/sage/rings/number_field/number_field.py
@@ -1438,18 +1438,18 @@ def _convert_map_from_(self, other):
             i - a
 
         """
-        from sage.categories.map import is_Map
+        from sage.categories.map import Map
         if self._structure is not None:
             structure = self.structure()
             if len(structure) >= 2:
                 to_self = structure[1]
-                if is_Map(to_self) and to_self.domain() is other:
+                if isinstance(to_self, Map) and to_self.domain() is other:
                     return to_self
         if isinstance(other, NumberField_generic) and other._structure is not None:
             structure = other.structure()
             if len(structure) >= 1:
                 from_other = structure[0]
-                if is_Map(from_other) and from_other.codomain() is self:
+                if isinstance(from_other, Map) and from_other.codomain() is self:
                     return from_other
 
     @cached_method
@@ -9956,8 +9956,8 @@ def relativize(self, alpha, names, structure=None):
         from sage.matrix.constructor import matrix
         from sage.modules.free_module_element import vector
 
-        from sage.categories.map import is_Map
-        if is_Map(alpha):
+        from sage.categories.map import Map
+        if isinstance(alpha, Map):
             # alpha better be a morphism with codomain self
             if alpha.codomain() != self:
                 raise ValueError("Co-domain of morphism must be self")
diff --git a/src/sage/rings/number_field/number_field_rel.py b/src/sage/rings/number_field/number_field_rel.py
index 7d7c150d9d0..8516d628f04 100644
--- a/src/sage/rings/number_field/number_field_rel.py
+++ b/src/sage/rings/number_field/number_field_rel.py
@@ -77,7 +77,7 @@
 
 import sage.libs.ntl.all as ntl
 
-from sage.categories.map import is_Map
+from sage.categories.map import Map
 from sage.structure.sequence import Sequence
 
 import sage.structure.parent_gens
@@ -2678,7 +2678,7 @@ def relativize(self, alpha, names):
         K = self.absolute_field('a')
         from_K, to_K = K.structure()
 
-        if is_Map(alpha):
+        if isinstance(alpha, Map):
             # alpha is an embedding of a subfield into self; compose to get an
             # embedding of a subfield into the absolute field
             beta = to_K * alpha
diff --git a/src/sage/sets/image_set.py b/src/sage/sets/image_set.py
index 07ef2de695d..e2780d523c8 100644
--- a/src/sage/sets/image_set.py
+++ b/src/sage/sets/image_set.py
@@ -18,7 +18,7 @@
 
 from typing import Iterator
 
-from sage.categories.map import is_Map
+from sage.categories.map import Map
 from sage.categories.poor_man_map import PoorManMap
 from sage.categories.sets_cat import Sets
 from sage.categories.enumerated_sets import EnumeratedSets
@@ -86,7 +86,7 @@ def __init__(self, map, domain_subset, *, category=None, is_injective=None, inve
             from sage.sets.set import Set
             domain_subset = Set(domain_subset)
 
-        if not is_Map(map) and not isinstance(map, PoorManMap):
+        if not isinstance(map, Map) and not isinstance(map, PoorManMap):
             map_name = f"The map {map}"
             if isinstance(map, Expression) and map.is_callable():
                 domain = map.parent().base()
@@ -100,7 +100,7 @@ def map(arg):
                 domain = domain_subset
             map = PoorManMap(map, domain, name=map_name)
 
-        if is_Map(map):
+        if isinstance(map, Map):
             map_category = map.category_for()
             if is_injective is None:
                 try:
diff --git a/src/sage/topology/simplicial_complex_morphism.py b/src/sage/topology/simplicial_complex_morphism.py
index c39bba0d355..e1f87f3ddd2 100644
--- a/src/sage/topology/simplicial_complex_morphism.py
+++ b/src/sage/topology/simplicial_complex_morphism.py
@@ -126,9 +126,17 @@ def is_SimplicialComplexMorphism(x):
         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)