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@inproceedings{Funk2011CharacterizationsOM, title={Characterizations of Morita equivalent inverse semigroups}, author={Jonathon A. Funk and Mark V. Lawson and Benjamin Steinberg}, year={2011} }

- Published 2011
DOI:10.1016/j.jpaa.2011.02.015

For a fixed inverse semigroup S, there are two natural categories of left actions of S: the category Fact of unitary actions of S on sets X meaning actions where SX = X, and the category Étale of étale actions meaning those unitary actions equipped with a function p : X → E(S), to the set of idempotents of S, such that p(x)x = x and p(sx) = ses∗, where s∗ denotes the inverse of s. The category Étale can be regarded as the classifying topos of S. There is a forgetful functor U from Étale to Fact… CONTINUE READING