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Type: Journal article
Title: On certain 2-categories admitting localisation by bicategories of fractions
Author: Roberts, D.
Citation: Applied Categorical Structures: a journal devoted to applications of categorical methods in algebra, analysis, order, topology and computer science, 2016; 24(4):373-384
Publisher: Springer Verlag (Germany)
Issue Date: 2016
ISSN: 1572-9095
Statement of
David Michael Roberts
Abstract: Pronk's theorem on bicategories of fractions is applied, in almost all cases in the literature, to 2-categories of geometrically presentable stacks on a 1-site. We give an proof that subsumes all previous such results and which is purely 2-categorical in nature, ignoring the nature of the objects involved. The proof holds for 2-categories that are not (2,1)-categories, and we give conditions for local essential smallness.
Keywords: 2-categories; Bicategories of fractions; Localization; Stacks
Rights: © The Author(s) 2015. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
DOI: 10.1007/s10485-015-9400-4
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Mathematical Sciences publications

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