Some categorical equivalences for 𝐸-unitary inverse semigroups
Mario Petrich · Transactions of the American Mathematical Society · 1980
The structure of E -unitary inverse semigroups has been described by McAlister and by Reilly and the author. The parameters in the first structure theorem may be made into a category, and the same holds for the parameters in the second structure theorem. We prove that each of these categories is equivalent to the category of E -unitary inverse semigroups and their homomorphisms. We also provide functors between the two first-mentioned categories which are naturally equivalent to the composition of the functors figuring in the categorical equivalence referred to above.