- {\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...
- 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...
- _{R}-:{\text{Mod-}}R\times R{\text{-Mod}}\longrightarrow \mathrm {Ab} } is a
bifunctor which accepts a
right and a left R
module pair as input, and ****igns them...
- 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...
-
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...
-
called vertical composition;
given three objects a, b and c,
there is a
bifunctor ∗ : B ( b , c ) × B ( a , b ) → B ( a , c ) {\displaystyle *:\mathbf {B}...
- does not fit. First,
consider the
binary product functor,
which is a
bifunctor. For f 1 : X 1 → Y 1 , f 2 : X 2 → Y 2 {\displaystyle f_{1}:X_{1}\to Y_{1}...
