Some categorical equivalences for 𝐸-unitary inverse semigroups

Petrich, Mario

doi:10.1090/S0002-9947-1980-0567092-2

Some categorical equivalences for $E$-unitary inverse semigroups
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Trans. Amer. Math. Soc. 259 (1980), 493-503 Request permission

Abstract:

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.

References

D. B. McAlister, Groups, semilattices and inverse semigroups. I, II, Trans. Amer. Math. Soc. 192 (1974), 227–244; ibid. 196 (1974), 351–370. MR 357660, DOI 10.1090/S0002-9947-1974-0357660-2

Groups, semilattices and inverse semigroups

196

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