Isotropy and crossed toposes

Jonathon Funk, Pieter Hofstra and Benjamin Steinberg

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.

Keywords: Topos theory, inverse semigroups, \'etale groupoids, isotropy groups, crossed modules

2010 MSC: 18B25, 18B40, 18D05, 20L05, 20M18, 20M35, 22A22

Theory and Applications of Categories, Vol. 26, 2012, No. 24, pp 660-709.

Published 2012-11-16.

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