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Journal Article

Multitensor lifting and strictly unital higher category theory

MPS-Authors
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Batanin,  Michael
Max Planck Institute for Mathematics, Max Planck Society;

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Weber,  Mark
Max Planck Institute for Mathematics, Max Planck Society;

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http://www.tac.mta.ca/tac/volumes/28/25/28-25.pdf
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Citation

Batanin, M., Cisinski, D.-C., & Weber, M. (2013). Multitensor lifting and strictly unital higher category theory. Theory and Applications of Categories, 28: 25, pp. 804-856.


Cite as: https://hdl.handle.net/21.11116/0000-0006-95EF-5
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.