Applied Categorical Structures

, Volume 24, Issue 4, pp 373–384 | Cite as

On Certain 2-Categories Admitting Localisation by Bicategories of Fractions

  • David Michael Roberts


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. This is the published version of arXiv:1402.7108.


2-categories Bicategories of fractions Localization Stacks 

Mathematics Subject Classification (2010)

Primary 18D05 Secondary 18F10 18E35 


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Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of AdelaideAdelaideAustralia

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