Diagonal functor : The diagonal functor is defined as the functor from D to the functor category D C which sends each object in D to the constant f...

Preservation of limits Representable functors are naturally isomorphic to Hom functors and therefore share their properties. In particular, (covari...

Beck's monadicity theorem gives a characterization of monadic functors. [ edit ] Uses Monads are used in functional programming to express types of...

Functors Main article: functor Functors are structure-preserving maps between categories. They can be thought of as morphisms in the category of al...

Ab is injective if and only if it is divisible ; it is projective if and only if it is a free abelian group. The category has a projective generato...

Ab is a reflective subcategory of the category of groups , Grp . The reflector is the functor which sends each group to its abelianization . Simila...

It follows that if coproducts exists in a given category (they need not) they are unique up to a unique isomorphism that respects the injections. I...

Among other useful concepts are regular epimorphism , extremal epimorphism , strong epimorphism , and split epimorphism . A regular epimorphism coe...