THE LOCALIC ISOTROPY GROUP OF A TOPOS
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F18%3A00108286" target="_blank" >RIV/00216224:14310/18:00108286 - isvavai.cz</a>
Result on the web
<a href="http://www.tac.mta.ca/tac/volumes/33/41/33-41.pdf" target="_blank" >http://www.tac.mta.ca/tac/volumes/33/41/33-41.pdf</a>
DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
THE LOCALIC ISOTROPY GROUP OF A TOPOS
Original language description
It has been shown by J.Funk, P.Hofstra and B.Steinberg that any Grothendieck topos T is endowed with a canonical group object, called its isotropy group, which acts functorially on every object of the topos. We show that this group is in fact the group of points of a localic group object, called the localic isotropy group, which also acts on every object, and in fact also on every internal locale and on every T topos. This new localic isotropy group has better functoriality and stability property than the original version and sheds some light on the phenomenon of higher isotropy observed for the ordinary isotropy group. We prove in particular using a localic version of the isotropy quotient that any geometric morphism can be factored uniquely as a connected atomic geometric morphism followed by a so called "essentially anisotropic" geometric morphism, and that connected atomic morphisms are exactly the quotients by open isotropy actions, hence providing a form of Galois theory for general (unpointed) connected atomic geometric morphisms.
Czech name
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Czech description
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Classification
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
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/GBP201%2F12%2FG028" target="_blank" >GBP201/12/G028: Eduard Čech Institute for algebra, geometry and mathematical physics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Theory and Applications of Categories
ISSN
1201-561X
e-ISSN
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Volume of the periodical
33
Issue of the periodical within the volume
2018
Country of publishing house
CA - CANADA
Number of pages
28
Pages from-to
1318-1345
UT code for WoS article
000509270800018
EID of the result in the Scopus database
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