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Internal Categorical Structures in Homotopical Algebra

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Towards Higher Categories

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

Abstract

This is a survey on the use of some internal higher categorical structures in algebraic topology and homotopy theory. After providing a general view of the area and its applications, we concentrate on the algebraic modelling of connected (n+1)-types through catn-groups.

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Acknowledgments

I am grateful to the organizers of the conference “n-Categories: Foundations and Applications” for the opportunity to speak on this topic. I also thank my colleagues at SUNY at Buffalo, where most of this paper was written, for providing a conducive working environment. I thank Ross Street for reading the final version and Peter May for helpful comments. I finally extend my gratitude to the many mathematicians I came in contact with from the time of my graduate studies until now, for enriching my understanding of the area of mathematics covered in this paper.

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Authors and Affiliations

  1. Department of Mathematics, Macquarie University, 2109, NSW, Australia

    Simona Paoli

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  1. Simona Paoli
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Correspondence to Simona Paoli .

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Editors and Affiliations

  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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Paoli, S. (2010). Internal Categorical Structures in Homotopical Algebra. 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_3

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