Abstract
A category C consists of the following data:
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a)
A set of ObC whose elements are called objects of C.
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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.
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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.
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© 1996 Springer-Verlag Berlin Heidelberg
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Gelfand, S.I., Manin, Y.I. (1996). Main Notions of the Category Theory. In: Methods of Homological Algebra. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03220-6_2
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DOI: https://doi.org/10.1007/978-3-662-03220-6_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-03222-0
Online ISBN: 978-3-662-03220-6
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