On Thu, Nov 24, 2005 at 10:34:08PM -0500, Topos8@aol.com wrote:
I don't like the term "semigroupoids" because it evokes (for me) the notion of invertibility which I want to avoid.
Google's not a perfect metric for popularity, but it returns about 350 hits for "semigroupoid", about 10 for "fair category", and none for "near category" (the one hit it returns is spurious). Wikipedia has an entry for "semigroupoid" (with the definition you're thinking of) and nothing on any of the others. Looking at MathSciNet, we find 180 hits for "semigroupoid", none for "fair category", and one for "near category". It's worse than that, though, because that paper uses "near category" to mean something different, namely a category-like object with identities but without associativity! All this suggests to me that "semigroupoid" is the standard term, and certainly it's the only one I've ever heard before. I don't think you need to worry about implied invertibility: if you know what both a groupoid and a semigroup are, the term "semigroupoid" strongly suggests a multi-object structure with associatively-composable arrows, but not necessarily with identities. At least, it suggests that to me :-) Hope that helps, Miles -- If you want to see your plays performed the way you wrote them, become President. -- Vaclav Havel