Algebra V pp 22-52 | Cite as

The Language of Categories

  • A. I. Kostrikin
  • I. R. Shafarevich
Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 38)

Abstract

A category C is the following collection of data:
  1. a.

    A class Ob C whose elements are called objects of the category C.

     
  2. b.

    A family of sets Hom(X, Y) (sometimes denoted also Hom c (X, Y)), one for each ordered pair X, Y ∈ Ob C; elements of Hom(X, Y) are called morphisms (from X to Y) and denoted ϕ: XY.

     
  3. c.

    A family of mappings Hom(X, Y) x Hom(Y, X)→ Hom(X, Y), one for each ordered triple of objects X, Y Z. To pair ϕ : XY, Ψ : YZ such a mapping associates a morphism denoted Ψοϕ or Ψϕ : XZ, called the composition of ϕ and Ψ.

     

Keywords

Exact Sequence Hopf Algebra Spectral Sequence Homology Group Cohomology Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • A. I. Kostrikin
    • 1
  • I. R. Shafarevich
    • 1
  1. 1.Steklov Mathematical InstituteMoscowRussia

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