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...

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...

{\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...

{\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 , − )...

tensor-hom adjunction is that the tensor product − ⊗ X {\displaystyle -\otimes X} and hom-functor Hom ⁡ ( X , − ) {\displaystyle \operatorname {Hom} (X,-)}...

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...

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...

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...

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...

Thus the contravariant hom-functor changes coproducts into products. Stated another way, the hom-functor, viewed as a functor from the opposite category...