Re: semigroups with many objects

Jacobson coined "rng" for a ring without identity and Bill returned the favor by proposing "rig" for a ring without negation (at least Bill's proposal can be pronounced). Alas, "catgory" is the only approximation for the instant case -- the only one, that is, if you refuse to count "ctegory" (category without automorphisms). Seriously though, "semi-category" is the one proposal not needing explanation. May I suggest that its very obviousness is why it was avoided.