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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Applied Categorical Structures

ISSN

0927-2852

e-ISSN

—

Svazek periodika

28

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

28

Strana od-do

935-962

Kód UT WoS článku

000561696300002

EID výsledku v databázi Scopus

2-s2.0-85089683577