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Toposes for semigroups: an invitation
Authors:Funk  Jonathon  Hofstra  Pieter
Institution:1.Department of Mathematics and Computer Science, CUNY Queensborough Community College, Bayside, New York City, NY, USA
;2.Department of Mathematics and Statistics, University of Ottawa, 150 Louis-Pasteur Pvt, Ottawa, ON, K1N 6N5, Canada
;
Abstract:

This is an expository paper in which we explain the basic ideas of topos theory in connection with semigroup theory. We focus mainly on the classifying topos of an inverse semigroup or pseudogroup, and to some extent on creating a dictionary between the language of semigroups and topos theory. We begin with the algebraic theory having to do with inverse semigroups, and then turn to an analysis of pseudogroups using sheaf theory. Our work includes some new material on wide semigroup homomorphisms and their geometric morphisms.

Keywords:
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