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

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

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...

For example: if there are objects (a,b,f1) (a',b',f1') (a,b,f2) (a',b',f2') in the comma category, then there could be g:a->a' h:b->b' s.t. (g,h) i...