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...

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...

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...

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

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...

P. Freyd [1] ) if it contains all the objects of C . A lluf subcategory is typically not full: the only full lluf subcategory of a category is that...