C ) can be made precise in several ways; the most succinct formulation uses the language of adjoint functors . Every functor F  : D ? E induces a f...

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...

It follows that any functor which preserves limits will take terminal objects to terminal objects, and any functor which preserves colimits will ta...

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

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...

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...

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...

Namely, we can demand the existence of a tensor product that is left adjoint to the internal Hom functor . In this approach, closed monoidal catego...

Zero morphism - Wikipedia, the free encyclopedia Zero morphism From Wikipedia, the free encyclopedia Jump to: navigation , search In category theor...

Category of preordered sets - Wikipedia, the free encyclopedia Category of preordered sets From Wikipedia, the free encyclopedia Jump to: navigatio...

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