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...

Yoneda's lemma asserts that every natural transformation between Hom functors is of this form. In other words, the Hom functors give rise to a full...

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

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...

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

Problems formulated with adjoint functors 1.3 Adjoint functors as solving optimization problems 1.4 The case of partial orders 2 Formal definitions...

G -sets are nothing but functors from this category to Set The category of all directed graphs is cartesian closed; this is a functor category as e...

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...

Limits and universal morphisms Colimits in comma categories may be "inherited". If and are cocomplete, is a cocontinuous functor, and another funct...

R -Mod, an injective object is an injective module . R -Mod has injective hulls (as a consequence, R-Mod has enough injectives). In the category of...