Abstract
In this paper, we mainly investigate Morita-like equivalence and Morita context for right fair semigroups. If two right fair semigroups S and T are Morita-like equivalent, that is, there is a category equivalence F : US − Act : UT-Act : G, we characterize the two functors F and G using Hom functor and tense product functor. Also, we investigate Morita context for right fair semigroups and obtain equivalence between two right unitary act categories.
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