An Introduction to Category Theory

  • Ernest G. Manes
  • Michael A. Arbib
Part of the Texts and Monographs in Computer Science book series (MCS)


Going beyond the partial functions and multifunctions already considered, one might invent other useful notions of the input/output function from X to Y. In addition to the need to considerX, Y as “data structures,” there are theoretical approaches to semantics in which all X, Y must carry further structure. Rather than embark on the misguided task of presenting an exhaustive list of present and future possibilities, we introducecategories as a framework for semantics which possess so little structure that most models of semantics can be represented this way. Surprisingly, what structure remains can be extensively developed and there is a great deal to say.


Disjoint Union Partial Function Category Theory Full Subcategory Total Function 
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Notes and References for Chapter 2

  1. M. A. Arbib and E. G. Manes, Arrows, Structures, and Functors: The Categorical Imperative, Academic Press, 1975.MATHGoogle Scholar
  2. J. Adámek, Theory of Mathematical Structures, D. Reidel, Dordrecht, 1983.MATHGoogle Scholar
  3. P. Freyd, Abelian Categories, Harper & Row, 1964.MATHGoogle Scholar
  4. H. Herrlich and G. E. Strecker, Category Theory, 2nd ed., Heldermann Verlag, Berlin, 1979.MATHGoogle Scholar
  5. S. Mac Lane, Categories for the Working Mathematician, Springer-Verlag, 1972.Google Scholar
  6. B. Mitchell, Theory of Categories, Academic Press, 1965.MATHGoogle Scholar
  7. R. Goldblatt, Topoi, The Categorial Analysis of Logic, Revised Edition, North-Holland, 1984.MATHGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1986

Authors and Affiliations

  • Ernest G. Manes
    • 1
  • Michael A. Arbib
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of MassachusettsAmherstUSA
  2. 2.Departments of Computer Science, Neurobiology and PhysiologyUniversity of Southern CaliforniaLos AngelesUSA

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