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Inverse semigroups with certain universal properties

Published online by Cambridge University Press:  09 April 2009

H. Lausch
H. Lausch
Affiliation:
Department of MathematicsMonash University Clayton, Vic. 3168, Australia.
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Free groups and free inverse semigroups are characterized by certain properties which are usually called universal. Category-theoretically they arise from left adjoints of forgetful functors which assign to each structure its underlying set. The purpose of this note is to give a construction of a wealth of inverse semigroups with certain universal properties which subsumes free groups and free inverse semigroups and incidentally elucidates some well-known constructions of free inverse semigroups (Scheiblich (1972)). Categorytheoretical terminology will be freely taken from (Mac Lane (1971)).

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 21 , Issue 2 , March 1976 , pp. 166 - 170
Copyright
Copyright © Australian Mathematical Society 1976

References

Lane, S. Mac (1971), Categories for the Working Mathematician (Springer, New York-Heidelberg-Berlin 1971).CrossRefGoogle Scholar
Munn, W. D. (1966), ‘Uniform semilattices and bisimple inverse semigroups’, Quart. J. Math. Oxford Ser. 17, 151–159.Google Scholar
Scheiblich, H. E. (1972), ‘Free inverse semigroups’, Semigroup F⊙rum 4, 351–359.CrossRefGoogle Scholar