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...

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

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...

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...

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

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

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...

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

Final topology - Wikipedia, the free encyclopedia Final topology From Wikipedia, the free encyclopedia Jump to: navigation , search In general topo...

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...