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Ordered groupoids and left cancellative categories. (English) Zbl 1053.18001

Denote by \(\mathcal{LC}\) the category of left cancellative categories and their functors and by \(\mathcal{OG}\) the category of ordered groupoids and ordered functors, respectively. The author constructs functors \(\mathbf G:\mathcal{LC}\to \mathcal{OG}\) and \(\mathbf C:\mathcal{OG}\to \mathcal{LC}\) such that for every \(C\in\mathcal{LC}\), there exists a full, dense embedding \(C\to\mathbf{CG}(C)\). Discussing relationship between \(G\in\mathcal{OG}\) and \(\mathbf{GC}(G)\), the author shows, for example, that if \(G\) has maximal identities, then \(\mathbf{GC}(G)\) is an enlargement of \(G\).

MSC:

18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories)
20M18 Inverse semigroups
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