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arXiv · 1805.05248

A localization of bicategories via homotopies

M. E. Descotte·E. J. Dubuc·M. Szyld
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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.

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M. E. Descotte, E. J. Dubuc, M. Szyld. 2018-05-14. A localization of bicategories via homotopies. https://arxiv.org/abs/1805.05248

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