- {\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...
- Let I be a
finite category and J be a
small filtered category. For any
bifunctor F : I × J → S e t , {\displaystyle F:I\times J\to \mathbf {Set} ,} there...
- category) is a
category C {\displaystyle \mathbf {C} }
equipped with a
bifunctor ⊗ : C × C → C {\displaystyle \otimes :\mathbf {C} \times \mathbf {C} \to...
- or map object. It
appears in one way as the
representation canonical bifunctor; but as (single) functor, of type [ X , − ] {\displaystyle [X,-]} , it...
- they are
given by
groupoids A {\displaystyle \mathbb {A} }
which have a
bifunctor + : A × A → A {\displaystyle +:\mathbb {A} \times \mathbb {A} \to \mathbb...
-
structure the map is a
covering space onto its image. Indeed, it is a
bifunctor in G and X. In
classical field theory, such a
section σ {\displaystyle...
-
noncommutative topology. KK-theory was
followed by a
series of
similar bifunctor constructions such as the E-theory and the
bivariant periodic cyclic theory...
- {\text{hom}}_{\mathcal {D}}(-,G-)} as functors. In fact, they are both
bifunctors from D op × C {\displaystyle {\mathcal {D}}^{\text{op}}\times {\mathcal...
