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...

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...

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

Subcategory Faithful functor Full functor Forgetful functor Yoneda lemma Representable functor Functor category Adjoint functors Galois connection ...

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...

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