1.NounA mapping between categories that is just like a functor except that
f
(
x
∘
y
)
=
f
(
x
)
∘
f
(
y
)
{\displaystyle f(x\circ y)=f(x)\circ f(y)}
and
f
(
1
)
=
1
{\displaystyle f(1)=1}
do not hold as exact equalities but only up to coherent isomorphisms.