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Can someone please give a reference for the definition stated here? Udoh (talk)

http://books.google.com/books?id=1O4pQgWM_DwC&pg=PA9&dq=semigroupoid&client=safari&cd=5#v=onepage&q=semigroupoid&f=false AshtonBenson (talk) 20:39, 3 January 2010 (UTC)[reply]

it doesn't say that it has to be small and neither does [1]. JMP EAX (talk) 22:33, 23 August 2014 (UTC)[reply]

The sole source cited is a paper about finite semigroups. So it's not surprising that it doesn't give a more general definition. Also, the paper is somewhat misleadingly cited on the wikipage as just the volume in which it appears, thus omitting the paper's title which would have made the context rather more obvious; the citation is also omitting the actual author of the paper, but that's not terribly germane on the issue of the definition. Some1Redirects4You (talk) 12:12, 20 April 2015 (UTC)[reply]

Also semicategory redirects here, but it' not mentioned and it doesn't appear to be exactly the same thing, at least not to all authors. On source says "a diagrammatizable semigroupoid is called a semicategory" [2]. But I can't see the rest in GB so I don't know what they mean by "diagrammatizable". Another source [3] cites the semicategory def from some other paper that I can't find yet, but given that they give different examples for the two notions, they can't be the same under the defs assumed there. JMP EAX (talk) 22:42, 23 August 2014 (UTC)[reply]

Yet there's a source (abstract is in French, but the rest is in English) which defines it exactly as a semigroupoid (sans small) [4]. JMP EAX (talk) 22:48, 23 August 2014 (UTC)[reply]

And like that isn't enough variation, [5] says: "In the case of semigroups, the natural extension is the notion of “category without identity”, also called “semigroupoid” by Tilson. Since both terms seem to be unfortunate— the first one is too negative and the second one too technical—, we take the risk of introducing the new terminology of quiver for these objects. “Quiver” is the translation of the French word carquois, which was originally chosen by the authors. It is meant to be as descriptive as possible, in the sense that a quiver “contains a bunch of arrows”." JMP EAX (talk) 17:29, 2 September 2014 (UTC)[reply]

Although the authors don't say it, it seems to match the graph notion of quiver. JMP EAX (talk) 17:32, 2 September 2014 (UTC)[reply]