Main Notions of the Category Theory
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A class ObC whose elements are called objects of C.
A collection of sets Hom(X, Y), one for each ordered pair of objects X, Y ∈ ObC, whose elements are called morphisms (from X to Y); they are denoted by ϕ: X → Y.
- c)A collection of mappingsone for each ordered triple of objects X,Y,Z ∈ ObC. Any mapping in this collection associates with a pair ϕ: X → Y, ψ: Y → Z a morphism from X to Z, denoted by ψ ◦ ϕ or ψϕ: X → Z, and called the composition or product of ϕ and ψ.$$ Hom(X,Y) \times Hom(Y,Z) \to Hom(X,Z), $$
KeywordsAbelian Group Exact Sequence Category Theory Full Subcategory Abelian Category
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