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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F20%3A00533367" target="_blank" >RIV/67985840:_____/20:00533367 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s10485-020-09605-x" target="_blank" >https://doi.org/10.1007/s10485-020-09605-x</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10485-020-09605-x" target="_blank" >10.1007/s10485-020-09605-x</a>

Result language
angličtina
Original language name
Gabriel–Ulmer duality for topoi and its relation with site presentations
Original language description
Let κ be a regular cardinal. We study Gabriel–Ulmer duality when one restricts the 2-category of locally κ-presentable categories with κ-accessible right adjoints to its locally full sub-2-category of κ-presentable Grothendieck topoi with geometric κ-accessible morphisms. In particular, we provide a full understanding of the locally full sub-2-category of the 2-category of κ-small cocomplete categories with κ-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 κ-presentable Grothendieck topoi with geometric κ-accessible morphisms is a reflective sub-bicategory of the 2-category of weakly κ-ary sites [in the sense of Shulman (Theory Appl Categ 27:97–173, 2012)] with morphisms of sites.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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