Geodesic
Locally anisotropic toposes II
Theory and applications of categories, Tome 37 (2021), pp. 914-939

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Every Grothendieck topos has internal to it a canonical group object, called its isotropy. We continue our investigation of this group, focusing again on locally anisotropic toposes. Such a topos is one admitting an étale cover by an anisotropic topos. We present a structural analysis of this class of toposes by showing that a topos is locally anisotropic if and only if it is equivalent to the topos of actions of a connected groupoid internal to an anisotropic topos. In particular we may conclude that a locally anisotropic topos, whence an étendue, has isotropy rank at most one, meaning that its isotropy quotient has trivial isotropy.

Publié le :
Classification : 18B25, 18B40, 18E50, 18F10
Keywords: toposes, isotropy, Galois theory, inverse semigroups 
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     author = {Jonathon Funk and Pieter Hofstra},
     title = {Locally anisotropic toposes {II}},
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     year = {2021},
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Jonathon Funk; Pieter Hofstra. Locally anisotropic toposes II. Theory and applications of categories, Tome 37 (2021), pp. 914-939. http://geodesic.mathdoc.fr/item/TAC_2021_37_a26/