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An introduction to n-categories

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Category Theory and Computer Science (CTCS 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1290))

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Abstract

An n-category is some sort of algebraic structure consisting of objects, morphisms between objects, 2-morphisms between morphisms, and so on up to n-morphisms, together with various ways of composing them. We survey various concepts of n-category, with an emphasis on ‘weak’ n-categories, in which all rules governing the composition of j-morphisms hold only up to equivalence. (An n-morphism is an equivalence if it is invertible, while a j-morphism for j < n is an equivalence if it is invertible up to a (j + 1)-morphism that is an equivalence.) We discuss applications of weak n-categories to various subjects including homotopy theory and topological quantum field theory, and review the definition of weak n-categories recently proposed by Dolan and the author.

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Authors and Affiliations

  1. Department of Mathematics, University of California, 92521, Riverside, California, USA

    John C. Baez

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  1. John C. Baez
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Eugenio Moggi Giuseppe Rosolini

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© 1997 Springer-Verlag Berlin Heidelberg

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Baez, J.C. (1997). An introduction to n-categories. In: Moggi, E., Rosolini, G. (eds) Category Theory and Computer Science. CTCS 1997. Lecture Notes in Computer Science, vol 1290. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0026978

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  • DOI: https://doi.org/10.1007/BFb0026978

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63455-3

  • Online ISBN: 978-3-540-69552-3

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