General Mathematics

    

Hom-Sets Category

Authors: Shao-Dan Lee

Let C be a category. Suppose that the hom-sets of C is small. Let CH be a category consist of the hom-sets of C. Then we define a morphism of CH by a morphisms pair 〈ν,μ〉. Hence the morphism is monic if and only if ν is epi and μ is monic. An object HomC (P, E) ∈ CH is an injective object if and only if P is a projective object and E is an injective object. There exists a bifunctor T : (C ↓ A)op × (B ↓ C) → (Hom(A, B) ↓ CH). And the bifunctor T is bijective. There exist the products in CH if and only if there exist the products and coproducts in C. There exist the pullback in CH if and only if there exist the pushout and pullback in C.

Comments: 15 Pages.

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Submission history

[v1] 2022-05-25 22:19:31

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