Definition of Bifunctor. Meaning of Bifunctor. Synonyms of Bifunctor

Here you will find one or more explanations in English for the word Bifunctor. Also in the bottom left of the page several parts of wikipedia pages related to the word Bifunctor and, of course, Bifunctor synonyms and on the right images related to the word Bifunctor.

Definition of Bifunctor

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Meaning of Bifunctor from wikipedia

- (Fop)op=F{\displaystyle \left(F^{\mathrm {op} }\right)^{\mathrm {op} }=F}. A bifunctor (also known as a binary functor) is a functor whose domain is a product...
- B′. The commutativity of the above diagram implies that Hom(–, –) is a bifunctor from C × C to Set which is contravariant in the first argument and covariant...
- Cartesian product of two sets. Product categories are used to define bifunctors and multifunctors. The product category C × D has: as objects: pairs of...
- or map object. It appears in one way as the representation canonical bifunctor; but as (single) functor, of type [X, -], it appears as an adjoint functor...
- category) is a category C{\displaystyle \mathbf {C} } equipped with a bifunctor ⊗:C×C→C{\displaystyle \otimes :\mathbf {C} \times \mathbf {C} \to \mathbf...
- Let I be a finite category and J be a small filtered category. For any bifunctor F:I×J→Set,{\displaystyle F:I\times J\to \mathbf {Set} ,} there is a natural...
- does not fit. First, consider the binary product functor, which is a bifunctor. For f1:X1→Y1,f2:X2→Y2{\displaystyle f_{1}:X_{1}\to Y_{1},f_{2}:X_{2}\to...
- they are given by groupoids A {\displaystyle \mathbb {A} } which have a bifunctor + : A × A → A {\displaystyle +:\mathbb {A} \times \mathbb {A} \to \mathbb...
- In terms of category theory, this means that the tensor product is a bifunctor from the category of vector spaces to itself. If f and g are both injective...
- recognize homC(F–, –) and homD(–, G–) as functors. In fact, they are both bifunctors from Dop × C to Set (the category of sets). For details, see the article...