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

Diagonal functor : The diagonal functor is defined as the functor from D to the functor category D C which sends each object in D to the constant f...

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

contravariant functor is right exact if and only if it turns finite limits into colimits. A functor is exact if and only if it is both left exact a...

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 and is the operation on Y . Each type of algebraic structure has its own type of homomorphism. For specific definitions see: group homomorphism r...

Zero morphism - Wikipedia, the free encyclopedia Zero morphism From Wikipedia, the free encyclopedia Jump to: navigation , search In category theor...

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...

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

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...

As mentioned above, the category of all abelian groups is an abelian category. The category of all finitely generated abelian groups is also an abe...

C . (Recall that a category C is preadditive if all its morphism sets are Abelian groups and morphism composition is bilinear , i.e. if C is enrich...