Overview
A functor represents a map from one category to another. That is, given two categories {% C %} and {% D %}, a functor {% F %} maps objects {% c \in Obj(C) %} to objects {% d \in Obj(F) %}.
{% F:c \rightarrow d %}
{% F %} also maps morphisms, {% f %} in {% C %} to morphims in {% D %} such that
{% F(f): F(c) \rightarrow F(d) %}
Further
- {% F %} maps identity morphisms to identity morphisms
- {% F %} respects composition. That is {% F(f \circ g) = F(f) \circ F(g) %}