TY - JOUR
T1 - Multitensor lifting and strictly unital higher category theory
AU - Batanin, Michael
AU - Cisinski, Denis Charles
AU - Weber, Mark
N1 - 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.
PY - 2013/9/23
Y1 - 2013/9/23
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84884566282&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:84884566282
SN - 1201-561X
VL - 28
SP - 804
EP - 856
JO - Theory and Applications of Categories
JF - Theory and Applications of Categories
ER -