If there is a monoidal functor from a monoidal category M to a monoidal category N , then any category enriched over M can be reinterpreted as a ca...

Indeed, the term "zero object" originated in the study of preadditive categories like Ab , where the zero object is the zero group . A preadditive ...

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...

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...

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...

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

Ab is injective if and only if it is divisible ; it is projective if and only if it is a free abelian group. The category has a projective generato...

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...

Then the equaliser is again the entire domain X , since the universal quantification in the definition is vacuously true . [ edit ] Difference kern...

The functor category of all additive functors from this category to the category of abelian groups is isomorphic to the category of left modules ov...