F-inverse semigroups and toposes
Jonathon Funk · 2007
We focus on two aspects of how semigroups and toposes are related [1, 4]. Oneaspect has to do with “left *-semigroups,” and how to present the classifying toposB(T) of an inverse semigroup T in semigroup terms. The other is a ‘dictionary’project connecting semigroup theory and topos theory. For instance, we explain thatif a semigroup T is F-inverse [3], then B(T) has a torsion-free generator that is locallysplit [2].References[1] J. Funk, Semigroups and toposes, Semigroup Forum, 1-41, 2007.[2] A. Kock and I. Moerdijk, Presentations of ´etendues, Cahiers de Top. et G´eom.Diff. Cat´egoriques, 32(2):145-164, 1991.[3] Mark V. Lawson, Inverse Semigroups: The Theory of Partial Symmetries, WorldScientific Publishing Co., Singapore, 1998.[4] M. Lawson and B. Steinberg, Etendues and ordered groupoids, Cahiers de Top.et G´eom. Diff. Cat´egoriques, 40(2):127-140, 2002.1