Abstract
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.
Received September 22, 1965.
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References
Bourbaki, N.: Eléments de mathématique. Livre I, Théorie des ensembles, chap. 4. Paris 1957.
— Eléments de mathématique. Algèbre commutative, chap. 6. Paris 1964.
Cohn, P. M.: Universal Algebra. New York 1965.
Eckmann, B., and P. J. Hilton: Group-like structures in general categories I. Math. Ann. 145, 227–255 (1962).
Fischer, H. R.: Limesräume. Math. Ann. 137, 269–303 (1959).
Goldie, A. W.: The Jordan-Hölder Theorem for general abstract algebras. Proc. London Math. Soc. (2) 52, 107–131 (1951).
Hofmann, F.: Über eine die Kategorie der Gruppen umfassende Kategorie. S.ber. Bayer. Akad. Wiss., Math.-Naturw. Klasse, 1960, 163-204.
Isbell, J. R.: Some remarks concerning categories and subspaces. Canad. J. Math. 9, 563–577 (1957).
Lawvere, F. W.: Functorial Semantics of Algebraic Theories. Thesis, Columbia University, 1963.
Linton, F. E. J.: The Functorial Foundations of Measure Theory. Thesis, Columbia University, 1963.
Wyler, O.: Categories of Structures. Univ. of New Mexico Technical Report No. 32, April 1963.
— Weakly exact categories. To appear in Archiv der Mathematik.
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Wyler, O. (1966). Operational Categories. In: Eilenberg, S., Harrison, D.K., MacLane, S., Röhrl, H. (eds) Proceedings of the Conference on Categorical Algebra. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-99902-4_13
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