Geodesic
Isotropy and crossed toposes
Theory and applications of categories, Tome 26 (2012), pp. 660-709

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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.

Publié le :
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},
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     year = {2012},
     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/