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...

A bimorphism is a morphism that is both an epimorphism and a monomorphism. Isomorphism : f  : X ? Y is called an isomorphism if there exists a morp...

Pullback of sieves The most common operation on a sieve is pullback . Pulling back a sieve S on c by an arrow f : c ?? c gives a new sieve f * S on...

Ab is a reflective subcategory of the category of groups , Grp . The reflector is the functor which sends each group to its abelianization . Simila...

X i , f ij ) be a direct system of objects and morphisms in a category C (same definition as above). The direct limit of this system is an object X...

In practice, for a valid statement about a particular category , the dual statement is valid in the dual category ( ). [ edit ] Duality The example...

Subobject classifier - Wikipedia, the free encyclopedia Subobject classifier From Wikipedia, the free encyclopedia Jump to: navigation , search In ...