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

Universal cones Limits and colimits are defined as universal cones . That is, cones through which all other cones factor. A cone ? from L to F is a...

If there is a monoidal functor from a monoidal category M to a monoidal category N , then any category enriched over M can be reinterpreted as a ca...

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

A bimorphism is a morphism that is both an epimorphism and a monomorphism. Isomorphism : f  : X ? Y is called an isomorphism if there exists a morp...

R -Mod, an injective object is an injective module . R -Mod has injective hulls (as a consequence, R-Mod has enough injectives). In the category of...

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

Categorical logic originated with Bill Lawvere 's Functorial Semantics of Algebraic Theories (1963), and Elementary Theory of the Category of Sets ...

The dual concept to that of kernel is that of cokernel . That is, the kernel of a morphism is its cokernel in the opposite category , and vice vers...

If the diagram is contravariant then it is called an inverse system . [ edit ] Cones and limits A cone of a diagram D  : J ? C is a morphism from t...

G -sets are nothing but functors from this category to Set The category of all directed graphs is cartesian closed; this is a functor category as e...

Subcategory Faithful functor Full functor Forgetful functor Yoneda lemma Representable functor Functor category Adjoint functors Galois connection ...