Functors Main article: functor Functors are structure-preserving maps between categories. They can be thought of as morp...
Diagonal functor : The diagonal functor is defined as the functor from D to the functor category D C which sends each ob...
Problems formulated with adjoint functors 1.3 Adjoint functors as solving optimization problems 1.4 The case of partial ...
Preservation of limits Representable functors are naturally isomorphic to Hom functors and therefore share their propert...
Yoneda's lemma asserts that every natural transformation between Hom functors is of this form. In other words, the Hom f...
C ) can be made precise in several ways; the most succinct formulation uses the language of adjoint functors . Every fun...
Limits and universal morphisms Colimits in comma categories may be "inherited". If and are cocomplete, is a co...
