Main Notions of the Category Theory

Sergei I. Gelfand () and Yuri I. Manin
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Sergei I. Gelfand: American Mathematical Society
Yuri I. Manin: MPI für Mathematik

Chapter Chapter II in Methods of Homological Algebra, 1996, pp 57-138 from Springer

Abstract: Abstract A category C consists of the following data: a) A set of ObC whose elements are called objects of C. b) 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 φ : Y → Y. c) A collection of mappings $$ Hom(X,Y)\;x\;Hom(Y,X) \to Hom(X,Z) $$ , one for each ordered triple of objects X, Y, Z ∈ ObC. Any mapping in this collection associates to a pair φ : X → Y, ψ : Y → Z a morphism from X to Z, denoted ψ ο φ or ψφ : X → Z, and called the composition or product of φ and ψ.

Keywords: Abelian Group; Topological Space; Category Theory; Abelian Category; Canonical Decomposition (search for similar items in EconPapers)
Date: 1996
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DOI: 10.1007/978-3-662-03220-6_2

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