Geodesic
Isotropy and crossed toposes
Theory and applications of categories, Tome 26 (2012), pp. 660-709 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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Motivated by constructions in the theory of inverse semigroups and etale groupoids, we define and investigate the concept of isotropy from a topos-theoretic perspective. Our main conceptual tool is a monad on the category of grouped toposes. Its algebras correspond to a generalized notion of crossed module, which we call a crossed topos. As an application, we present a topos-theoretic characterization and generalization of the `Clifford, fundamental' sequence associated with an inverse semigroup.

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Classification : 18B25, 18B40, 18D05, 20L05, 20M18, 20M35, 22A22
Keywords: Topos theory, inverse semigroups, \'etale groupoids, isotropy groups, crossed modules 
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     author = {Jonathon Funk and Pieter Hofstra and Benjamin Steinberg},
     title = {Isotropy and crossed toposes},
     journal = {Theory and applications of categories},
     pages = {660--709},
     year = {2012},
     volume = {26},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2012_26_a23/}
}
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Jonathon Funk; Pieter Hofstra; Benjamin Steinberg. Isotropy and crossed toposes. Theory and applications of categories, Tome 26 (2012), pp. 660-709. http://geodesic.mathdoc.fr/item/TAC_2012_26_a23/