Semigroups and ordered categories. I: The reduced case. (English) Zbl 0747.18007
Inverse semigroups can be described as groupoids (= small categories of isomorphisms) which are ordered in a special way. In particular, this order relation induces the structure of a semilattice on the set of idempotents of the groupoid. This idea can be generalized to regular semigroups. One has to consider a different type of inductive groupoid, where the idempotents acquire the structure of a regular biordered set. These known results and ideas serve as a starting point for the author. In this Part I of a longer paper main emphasis is on generalizing the above results on inverse semigroups. Groupoids are replaced by a more general kind of (ordered) categories.
Reviewer: B.M.Schein (Fayetteville)
MSC:
| 18B40 | Groupoids, semigroupoids, semigroups, groups (viewed as categories) |
| 20M50 | Connections of semigroups with homological algebra and category theory |
| 20M17 | Regular semigroups |
Keywords:
ordered small categories; abundant semigroups; \(U\)-semiabundant semigroups; regular semigroupsReferences:
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