Multitensor lifting and strictly unital higher category theory

Michael Batanin, Denis Charles Cisinski, Mark Weber

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    5 Citations (Scopus)
    23 Downloads (Pure)

    Abstract

    In this article we extend the theory of lax monoidal structures, also known as multitensors, and the monads on categories of enriched graphs that they give rise to. Our first principal result - the lifting theorem for multitensors - enables us to see the Gray tensor product of 2-categories and the Crans tensor product of Gray categories as part of this framework. We define weak n-categories with strict units by means of a notion of reduced higher operad, using the theory of algebraic weak factorisation systems. Our second principal result is to establish a lax tensor product on the category of weak n-categories with strict units, so that enriched categories with respect to this tensor product are exactly weak (n+1)-categories with strict units.

    Original languageEnglish
    Pages (from-to)804-856
    Number of pages53
    JournalTheory and Applications of Categories
    Volume28
    Publication statusPublished - 23 Sep 2013

    Bibliographical note

    Copyright the Author(s) 2013. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

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  • Cite this

    Batanin, M., Cisinski, D. C., & Weber, M. (2013). Multitensor lifting and strictly unital higher category theory. Theory and Applications of Categories, 28, 804-856.