Geodesic
A localization of bicategories via homotopies
Theory and applications of categories, Tome 35 (2020), pp. 845-874

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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.

Publié le :
Classification : 18N10, 18N40, 18N55
Keywords: localization, bicategory, homotopy 
@article{TAC_2020_35_a22,
     author = {Descotte M.E. and Dubuc E.J. and Szyld M.},
     title = {A localization of bicategories via homotopies},
     journal = {Theory and applications of categories},
     pages = {845--874},
     publisher = {mathdoc},
     volume = {35},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2020_35_a22/}
}
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Descotte M.E.; Dubuc E.J.; Szyld M. A localization of bicategories via homotopies. Theory and applications of categories, Tome 35 (2020), pp. 845-874. http://geodesic.mathdoc.fr/item/TAC_2020_35_a22/