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Partialization of categories and inverse braid-permutation monoids. (English) Zbl 1176.20062
There are several approaches to construction of inverse semigroups. The most abstract one is the categorical approach. This approach is based on the notions of a category of partial maps and a restriction category. In this paper, in Section 2, the authors give a short overview of this abstract categorical approach in the interpretation and they define the partialization functor. Then they give several examples from the theory of semigroups in Section 3. In particular, as a main example they work on the inverse braid monoid in Section 4. They obtain this monoid as one more application of the partialization functor. In Section 5, they generalize this main example and construct a new inverse monoid with topological origin. Finally, in Section 6, they go back to the abstract study of the partialization functor and they show that it is in fact an endofunctor of a certain category.

MSC:
20M50 Connections of semigroups with homological algebra and category theory
20M18 Inverse semigroups
20F36 Braid groups; Artin groups
18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphisms
18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories)
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