Morita-like equivalence for fair semigroups

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 $F:US-Act\rightleftharpoons:UT-Act:G,$  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.