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Title
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Gabriel-Ulmer duality for topoi and its relation with site presentations
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Author
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Abstract
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| 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. |
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Language
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English
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Source (journal)
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Applied categorical structures. - Dordrecht, 1993, currens
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Publication
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Dordrecht
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Springer
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2020
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ISSN
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0927-2852
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DOI
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10.1007/S10485-020-09605-X
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Volume/pages
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p. 1-28
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ISI
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000561696300002
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Full text (Publisher's DOI)
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Full text (publisher's version - intranet only)
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