Gabriel-Ulmer duality for topoi and its relation with site presentations

Let kappa be a regular cardinal. We study Gabriel-Ulmer duality when one restricts the 2-category of locally kappa-presentable categories with kappa-accessible right adjoints to its locally full sub-2-category of kappa-presentable Grothendieck topoi with geometric kappa-accessible morphisms. In particular, we provide a full understanding of the locally full sub-2-category of the 2-category of kappa-small cocomplete categories with kappa-small colimit preserving functors arising as the corresponding 2-category of presentations via the restriction. We analyse the relation of these presentations of Grothendieck topoi with site presentations and we show that the 2-category of locally kappa-presentable Grothendieck topoi with geometric kappa-accessible morphisms is a reflective sub-bicategory of the 2-category of weakly kappa-ary sites [in the sense of Shulman (Theory Appl Categ 27:97-173, 2012)] with morphisms of sites.

Publication year:2020

Keywords:A1 Journal article

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BOF-publication weight:0.5

CSS-citation score:1

Authors:International

Authors from:Higher Education

Accessibility:Closed