Characterizations of Morita equivalent inverse semigroups

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

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