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...

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...

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

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

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

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...

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...

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

Snake lemma - Wikipedia, the free encyclopedia Snake lemma From Wikipedia, the free encyclopedia Jump to: navigation , search In mathematics , part...