A localization of bicategories via homotopies
Abstract
Given a bicategory C and a family W of arrows of C, we give conditions on the pair (C,W) that allow us to construct the bicategorical localization with respect to W by dealing only with the 2-cells, that is without adding objects or arrows to C. We show that in this case, the 2-cells of the localization can be given by the homotopies with respect to W, a notion defined in this article which is closely related to Quillen's notion of homotopy for model categories but depends only on a single family of arrows. This localization result has a natural application to the construction of the homotopy bicategory of a model bicategory, which we develop elsewhere, as the pair (C_{fc},W) given by the weak equivalences between fibrant-cofibrant objects satisfies the conditions given in the present article.
Keywords
Cite
@article{arxiv.1805.05248,
title = {A localization of bicategories via homotopies},
author = {M. E. Descotte and E. J. Dubuc and M. Szyld},
journal= {arXiv preprint arXiv:1805.05248},
year = {2021}
}