n (mathematics) a structure-preserving
mapping between
categories: if
F is a functor from category
C to category
D, then
F maps objects of
C to objects of
D and morphisms of
C to morphisms of
D such that any morphism
f:
X→
Y of
C is mapped to a morphism
F(
f):
F(
X) →
F(
Y) of
D, such that if
then
, and such that identity morphisms (and only identity morphisms) are mapped to identity morphisms. Note: the functor just described is
covariant.