1.NounA functor which maps a morphism f:X → Y to a morphism F(f):F(Y) → F(X), such that if
h
=
g
∘
f
{\displaystyle h=g\circ f}
, then
F
(
h
)
=
F
(
f
)
∘
F
(
g
)
{\displaystyle F(h)=F(f)\circ F(g)}
.
"A contravariant functor
F
:
C
→
D
{\displaystyle F:{\mathcal {C}}\rightarrow {\mathcal {D}}}
is the same as a covariant functor
F
:
C
o
p
→
D
{\displaystyle F:{\mathcal {C}}^{op}\rightarrow {\mathcal {D}}}
."