Some of the things I've learned every day since Oct 10, 2016
January 10, 2017Posted by on
In category theory, a functor is a map between categories consisting of two components:
- a map from the objects of to those of
- a map from each morphism in to a morphism in .
This map must preserve the identity morphisms and composition. That is, it must satisfy the following properties:
- for objects in
Functors can be thought of as kinds of homomorphisms between categories. With functors as arrows, categories can then form a category called , the category of categories.