Operational Categories

  • Oswald Wyler
Conference paper


The present paper is an attempt to formulate at least part of the Bourbaki theory of “espèces de structures” (see [1]) in categorical terms. While our theory is far from including all “espèces de structures” found in Mathematics — for instance, categories of manifolds or of fiber bundles are excluded — it does include all or almost all “espèces de structures” found in Algebra, and many “espèces de structures” found in Topology.


Operational Category Inverse Image Complete Lattice Direct Limit Hausdorff Space 
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  1. [1]
    Bourbaki, N.: Eléments de mathématique. Livre I, Théorie des ensembles, chap. 4. Paris 1957.Google Scholar
  2. [2]
    — Eléments de mathématique. Algèbre commutative, chap. 6. Paris 1964.Google Scholar
  3. [3]
    Cohn, P. M.: Universal Algebra. New York 1965.Google Scholar
  4. [4]
    Eckmann, B., and P. J. Hilton: Group-like structures in general categories I. Math. Ann. 145, 227–255 (1962).MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    Fischer, H. R.: Limesräume. Math. Ann. 137, 269–303 (1959).MathSciNetMATHCrossRefGoogle Scholar
  6. [6]
    Goldie, A. W.: The Jordan-Hölder Theorem for general abstract algebras. Proc. London Math. Soc. (2) 52, 107–131 (1951).MathSciNetCrossRefGoogle Scholar
  7. [7]
    Hofmann, F.: Über eine die Kategorie der Gruppen umfassende Kategorie. S.ber. Bayer. Akad. Wiss., Math.-Naturw. Klasse, 1960, 163-204.Google Scholar
  8. [8]
    Isbell, J. R.: Some remarks concerning categories and subspaces. Canad. J. Math. 9, 563–577 (1957).MathSciNetMATHCrossRefGoogle Scholar
  9. [9]
    Lawvere, F. W.: Functorial Semantics of Algebraic Theories. Thesis, Columbia University, 1963.Google Scholar
  10. [10]
    Linton, F. E. J.: The Functorial Foundations of Measure Theory. Thesis, Columbia University, 1963.Google Scholar
  11. [11]
    Wyler, O.: Categories of Structures. Univ. of New Mexico Technical Report No. 32, April 1963.Google Scholar
  12. [12]
    — Weakly exact categories. To appear in Archiv der Mathematik.Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1966

Authors and Affiliations

  • Oswald Wyler
    • 1
  1. 1.Department of MathematicsCarnegie Institute of TechnologyPittsburgh 13USA

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