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

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

It follows that if coproducts exists in a given category (they need not) they are unique up to a unique isomorphism that respects the injections. I...

Categorical logic originated with Bill Lawvere 's Functorial Semantics of Algebraic Theories (1963), and Elementary Theory of the Category of Sets ...

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...

The dual concept to that of kernel is that of cokernel . That is, the kernel of a morphism is its cokernel in the opposite category , and vice vers...

If the diagram is contravariant then it is called an inverse system . [ edit ] Cones and limits A cone of a diagram D  : J ? C is a morphism from t...

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

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...

Simplicial category - Wikipedia, the free encyclopedia Simplicial category From Wikipedia, the free encyclopedia Jump to: navigation , search In ma...

Complete Heyting algebras arise as the Lindenbaum algebras of (intuitionistic) logics with infinite disjunction. [ edit ] Frames and locales The ob...

B , the pullback X × B E is a fiber bundle over X called the pullback bundle . The associated commutative diagram is a morphism of fiber bundles. I...