Lawson, Mark V. Ordered groupoids and left cancellative categories. (English) Zbl 1053.18001 Semigroup Forum 68, No. 3, 458-476 (2004). 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 \(G\). Reviewer: Peeter Normak (Tallinn) Cited in 11 Documents MSC: 18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories) 20M18 Inverse semigroups Keywords:ordered groupoid; left cancellative category; category of monics PDFBibTeX XMLCite \textit{M. V. Lawson}, Semigroup Forum 68, No. 3, 458--476 (2004; Zbl 1053.18001) Full Text: DOI