Group functor

Symbol-free definition
A group functor on a category is a functor from that category to the category of groups.

Definition with symbols
A group functor $$F$$ on a category $$C$$ is the following:


 * To every object $$A \in C$$, it associates a group $$F(A)$$
 * To every morphism $$f:A \to B$$ between objects in $$C$$, it associates a homomorphism $$F(f):F(A) \to F(B)$$

such that:


 * The group homomorphism associated to the identity morphism, is the identity map
 * The group homomorphism associated to the composite of two morphisms, is the composite of the associated group homomorphisms. That is, $$F(f \circ g) = F(f) \circ F(g)$$

Related notions

 * Group APS functor
 * Group IAPS functor