So.. yes map is a functor.
What is a functor example?
A bifunctor (also known as a binary functor) is a functor whose domain is a product category. For example, the Hom functor is of the type Cop × C → Set. It can be seen as a functor in two arguments. The Hom functor is a natural example; it is contravariant in one argument, covariant in the other.
Which one is a functor?
A functor is a mapping between categories. Given two categories, C and D, a functor F maps objects in C to objects in D — it's a function on objects. If a is an object in C, we'll write its image in D as F a (no parentheses). But a category is not just objects — it's objects and morphisms that connect them.
