hom-sets (i.e. sets of morphisms between objects) give rise to important functors to the category of sets. These functors are called hom-functors and...
9 KB (1,029 words) - 19:06, 4 March 2024
the group homomorphism Hom(f, g): Hom(A2, B1) → Hom(A1, B2) is given by φ ↦ g ∘ φ ∘ f. See Hom functor. Representable functors We can generalize the previous...
24 KB (3,513 words) - 02:56, 11 August 2024
{\displaystyle \mathrm {hom} _{\mathcal {C}}(FY,X)} , φ f {\displaystyle \varphi f} is the right adjunct of f {\displaystyle f} (p. 81). The functor F {\displaystyle...
63 KB (9,958 words) - 21:43, 1 August 2024
Yoneda lemma (redirect from Yoneda functor)
{\mathcal {C}}} gives rise to a natural functor to S e t {\displaystyle \mathbf {Set} } called a hom-functor. This functor is denoted: h A = H o m ( A , − )...
20 KB (3,362 words) - 13:43, 2 August 2024
tensor-hom adjunction is that the tensor product − ⊗ X {\displaystyle -\otimes X} and hom-functor Hom ( X , − ) {\displaystyle \operatorname {Hom} (X,-)}...
5 KB (912 words) - 14:09, 13 June 2024
Limit (category theory) (redirect from Continuous functor)
from the fact the covariant Hom functor Hom(N, –) : C → Set preserves all limits in C. By duality, the contravariant Hom functor must take colimits to limits...
28 KB (4,352 words) - 03:41, 22 March 2024
of sets. For each object A of C let Hom(A,–) be the hom functor that maps object X to the set Hom(A,X). A functor F : C → Set is said to be representable...
13 KB (1,889 words) - 11:12, 28 July 2024
In mathematics, the Ext functors are the derived functors of the Hom functor. Along with the Tor functor, Ext is one of the core concepts of homological...
19 KB (3,248 words) - 17:48, 21 August 2024
category theory, a faithful functor is a functor that is injective on hom-sets, and a full functor is surjective on hom-sets. A functor that has both properties...
4 KB (571 words) - 19:05, 4 March 2024
Thus the contravariant hom-functor changes coproducts into products. Stated another way, the hom-functor, viewed as a functor from the opposite category...
12 KB (2,129 words) - 00:42, 19 June 2024