Some categorical equivalences for -unitary inverse semigroups

Author:
Mario Petrich

Journal:
Trans. Amer. Math. Soc. **259** (1980), 493-503

MSC:
Primary 20M10; Secondary 18B10

DOI:
https://doi.org/10.1090/S0002-9947-1980-0567092-2

MathSciNet review:
567092

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Abstract | References | Similar Articles | Additional Information

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.

**[1]**D. B. McAlister,*Groups, semilattices and inverse semigroups*, Trans. Amer. Math. Soc.**192**(1974), 227-244. MR**0357660 (50:10128)****[2]**-,*Groups, semilattices and inverse semigroups*. II, Trans. Amer. Math. Soc.**196**(1974), 351-370.**[3]**S. Mac Lane,*Categories for the working mathematician*, Graduate Texts in Math., No. 5, Springer-Verlag, Berlin and New York, 1971. MR**0354798 (50:7275)****[4]**W. D. Munn,*A note on E-unitary inverse semigroups*, Bull. London Math. Soc.**8**(1976), 71-76. MR**0396809 (53:669)****[5]**W. D. Munn and N. R. Reilly,*E-unitary congruences on inverse semigroups*, Glasgow Math. J.**17**(1976), 57-75. MR**0404498 (53:8300)****[6]**M. Petrich and N. R. Reilly,*A representation of E-unitary inverse semigroups*, Quart. J. Math. (2)**30**(1979), 339-350. MR**545069 (80j:20067)****[7]**B. M. Schein,*A new proof for the McAlister P-theorem*, Semigroup Forum**10**(1975), 185-188. MR**0379716 (52:621)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1980-0567092-2

Keywords:
*E*-unitary inverse semigroups,
equivalence of categories,
McAlister triples,
unitary triples

Article copyright:
© Copyright 1980
American Mathematical Society