diff --git a/src/sage/algebras/lie_algebras/lie_algebra_element.pyx b/src/sage/algebras/lie_algebras/lie_algebra_element.pyx
index d54644647d8..d519d37b618 100644
--- a/src/sage/algebras/lie_algebras/lie_algebra_element.pyx
+++ b/src/sage/algebras/lie_algebras/lie_algebra_element.pyx
@@ -120,11 +120,9 @@ cdef class LieAlgebraElement(IndexedFreeModuleElement):
             return s
         names = self.parent().variable_names()
         if base_map is None:
-            return codomain.sum(c * t._im_gens_(codomain, im_gens, names)
-                                for t, c in self._monomial_coefficients.iteritems())
-        else:
-            return codomain.sum(base_map(c) * t._im_gens_(codomain, im_gens, names)
-                                for t, c in self._monomial_coefficients.iteritems())
+            base_map = lambda x: x
+        return codomain.sum(base_map(c) * t._im_gens_(codomain, im_gens, names)
+                            for t, c in self._monomial_coefficients.iteritems())
 
     cpdef lift(self):
         """
diff --git a/src/sage/algebras/lie_algebras/morphism.py b/src/sage/algebras/lie_algebras/morphism.py
index bea2d600b43..2ccf85263d7 100644
--- a/src/sage/algebras/lie_algebras/morphism.py
+++ b/src/sage/algebras/lie_algebras/morphism.py
@@ -23,6 +23,7 @@
 from sage.structure.richcmp import richcmp
 from sage.matrix.constructor import matrix
 from itertools import combinations
+from six import iteritems
 
 # TODO: Refactor out common functionality with RingHomomorphism_im_gens
 class LieAlgebraHomomorphism_im_gens(Morphism):
@@ -607,8 +608,7 @@ def _call_(self, x):
             1/3*A - 1/3*B + 2/3*C
         """
         C = self.codomain()
-        if self._base_map is None:
-            return C.sum(c * self._im_gens[i] for i, c in x.to_vector().iteritems())
-        else:
-            bh = self._base_map
-            return C.sum(bh(c) * self._im_gens[i] for i, c in x.to_vector().iteritems())
+        bh = self._base_map
+        if bh is None:
+            bh = lambda t: t
+        return C.sum(bh(c) * self._im_gens[i] for i, c in iteritems(x.to_vector()))
diff --git a/src/sage/quivers/representation.py b/src/sage/quivers/representation.py
index 60a6b680ee3..6512e879fc5 100644
--- a/src/sage/quivers/representation.py
+++ b/src/sage/quivers/representation.py
@@ -2425,7 +2425,7 @@ def algebraic_dual(self, basis=False):
         from sage.quivers.homspace import QuiverHomSpace
         return QuiverHomSpace(self, self._semigroup.free_module(self.base_ring())).left_module(basis)
 
-    def Hom(self, codomain):
+    def Hom(self, codomain, category=None):
         """
         Return the hom space from ``self`` to ``codomain``.
 
@@ -2438,7 +2438,7 @@ def Hom(self, codomain):
             Dimension 2 QuiverHomSpace
         """
         from sage.quivers.homspace import QuiverHomSpace
-        return QuiverHomSpace(self, codomain)
+        return QuiverHomSpace(self, codomain, category=category)
 
     def direct_sum(self, modules, return_maps=False):
         """
diff --git a/src/sage/rings/multi_power_series_ring_element.py b/src/sage/rings/multi_power_series_ring_element.py
index cb8ef6e2804..111a0bf525d 100644
--- a/src/sage/rings/multi_power_series_ring_element.py
+++ b/src/sage/rings/multi_power_series_ring_element.py
@@ -552,10 +552,10 @@ def _subs_formal(self, *x, **kwds):
 
         y = 0
         base_map = kwds.get('base_map')
+        if base_map is None:
+            base_map = lambda t: t
         for m, c in iteritems(self.dict()):
-            if base_map is not None:
-                c = base_map(c)
-            y += c*prod([x[i]**m[i] for i in range(n) if m[i] != 0])
+            y += base_map(c)*prod([x[i]**m[i] for i in range(n) if m[i] != 0])
         if self.prec() == infinity:
             return y
         else:
diff --git a/src/sage/structure/parent.pyx b/src/sage/structure/parent.pyx
index 6843929a38c..50ca7fa616c 100644
--- a/src/sage/structure/parent.pyx
+++ b/src/sage/structure/parent.pyx
@@ -1346,6 +1346,7 @@ cdef class Parent(sage.structure.category_object.CategoryObject):
             codomain = im_gens.universe()
         if isinstance(im_gens, Sequence_generic):
             im_gens = list(im_gens)
+        # Not all homsets accept catgory/check/base_map as arguments
         kwds = {}
         if check is not None:
             kwds['check'] = check
@@ -1358,7 +1359,8 @@ cdef class Parent(sage.structure.category_object.CategoryObject):
                 # so we conservatively choose just SetsWithPartialMaps
                 category = SetsWithPartialMaps()
             kwds['base_map'] = base_map
-        return self.Hom(codomain, category=category)(im_gens, **kwds)
+        Hom_kwds = {} if category is None else {'category': category}
+        return self.Hom(codomain, **Hom_kwds)(im_gens, **kwds)
 
     #################################################################################
     # New Coercion support functionality