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...

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...

Yoneda's lemma asserts that every natural transformation between Hom functors is of this form. In other words, the Hom functors give rise to a full...

Problems formulated with adjoint functors 1.3 Adjoint functors as solving optimization problems 1.4 The case of partial orders 2 Formal definitions...

Limits and universal morphisms Colimits in comma categories may be "inherited". If and are cocomplete, is a cocontinuous functor, and another funct...

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

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...

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...

I. Heim and A. Kratzer (1998). Semantics in Generative Grammar . Blackwell. [ edit ] External links Look up currying in Wiktionary , the free dicti...

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...

C . (Recall that a category C is preadditive if all its morphism sets are Abelian groups and morphism composition is bilinear , i.e. if C is enrich...