A double categorical model of weak 2-categories

Simona Paoli and Dorette Pronk

We introduce the notion of weakly globular double categories, a particular class of strict double categories, as a way to model weak 2-categories. We show that this model is suitably equivalent to bicategories and give an explicit description of the functors involved in this biequivalence. As an application we show that groupoidal weakly globular double categories model homotopy 2-types.

Keywords: double categories, strict 2-categories, bicategories, Tamsamani weak 2-categories, pseudo-functors, strictification

2010 MSC: 18D05, 18G55, 18G30

Theory and Applications of Categories, Vol. 28, 2013, No. 27, pp 933-980.

Published 2013-10-06.


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