Morita equivalence based on Morita context for arbitrary semigroups

Year 2016, Volume: 45 Issue: 4, 1083 - 1090, 01.08.2016

Hongxing Liu

Abstract

In this paper, we study the Morita context for arbitrary semigroups. We
prove that, for two semigroups S and T, if there exists a Morita context
$(S, T, P, Q, \tau, \mu)$ (not necessary unital) such that the maps $\tau$ and $\mu$ are
surjective, the categories U S -FAct and U T -FAct are equivalent. Using
this result, we generalize Theorem 2 in [2] to arbitrary semigroups.
Finally, we give a characterization of Morita context for semigroups.

Keywords

semigroup, Morita context, functor, category, S-act

References

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