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A 2-Categories Companion

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Book cover Towards Higher Categories

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 152))

Abstract

This paper is a rather informal guide to some of the basic theory of 2-categories and bicategories, including notions of limit and colimit, 2-dimensional universal algebra, formal category theory, and nerves of bicategories.

AMS(MOS) subject classifications. 18D05, 18C15, 18A30, 18G30, 18G55, 18C35.

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Acknowledgements

It is a pleasure to acknowledge support and encouragement from a number of sources. I am grateful to the Institute for Mathematics and its Applications, Minneapolis for hosting and supporting the workshop on higher categories in 2004, and to John Baez and Peter May who organized the workshop and who encouraged me to publish these notes. The material here was based on lectures I gave at the University of Chicago in 2006, at the invitation of Peter May and Eugenia Cheng. I’m grateful to them for their hospitality, and the interest that they and the topology/categories group at Chicago took in these lectures. I’m particularly grateful to Mike Shulman, whose excellent TeXed notes of the lectures were the basis for the companion.

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Authors and Affiliations

  1. School of Computing and Mathematics, University of Western Sydney, Locked Bag 1797, 1797, Penrith South DC, NSW, Australia

    Stephen Lack

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  1. Stephen Lack
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Correspondence to Stephen Lack .

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  1. Dept. Mathematics, University of California, Riverside, Riverside, 92521-0135, U.S.A.

    John C. Baez

  2. Dept. Mathematics, University of Chicago, East 58th Street University Ave. 1118, Chicago, 60637, U.S.A.

    J. Peter May

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Lack, S. (2010). A 2-Categories Companion. In: Baez, J., May, J. (eds) Towards Higher Categories. The IMA Volumes in Mathematics and its Applications, vol 152. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-1524-5_4

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