a structure-preserving mapping between groups: if F is a functor from group C to category D, after that F maps items of C to objects of D and morphisms of C to morphisms of D in a way that any morphism f:X→Y of C is mapped to a morphism F(f): F(X) → F(Y) of D, so that if after that , and so that identity morphisms (and just identification morphisms) are mapped to identity morphisms. Note: the functor only described is covariant.

One that does a surgical procedure or a function.

Grammar See work term.

a function term

a function item

a structure-preserving mapping between categories: if F is a functor from category C to category D, then F maps objects of C to objects of D and morphisms of C to morphisms of D such that any morphism f:X→Y of C is mapped to a morphism F(f): F(X) → F(Y) of D, such that if then , and such that identity morphisms (and only identity morphisms) are mapped to identity morphisms. Note: the functor just described is covariant.

## How would you define functor?