Categories and Functors

  • George M. Bergman
Part of the Universitext book series (UTX)


We define the concepts of category, functor, and morphism of functors (‘natural transformation’). The set-theoretic difficulty in treating cases like the category of all sets is handled using Grothendieck’s Axiom of Universes. Epimorphisms, monomorphisms, and similar concepts are investigated. The concept of “enriched categories” (for example, additive categories) is briefly sketched.


Abelian Group Topological Space Mathematical Object Homotopy Class Category Theory 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • George M. Bergman
    • 1
  1. 1.Department of MathematicsUniversity of California, BerkeleyBerkeleyUSA

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