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I am struggling with the notion of structure (for reasons related to Freiman's theory and normed rings), which is the main motivation for my question:

Could you suggest some (good) surveys or books with a systematic development of the theory of semicategories (starting from the basics), in the same spirit, say, of CWM and ACC?

I already checked nLab, and there is not really much about semicategories: The only reference given (click) doesn't provide background on the subject.

Thank you in advance,

Salvo

edited Sep 11 at 11:37

asked Sep 11 at 11:26

Salvo Tringali
819●2●7

	I believe these are also called semigroupoid, for which you'll find more references. – Jacques Carette Sep 11 at 12:23
	Sure, but nonetheless I can't find anything close to my expectations, and this is why I resolved to ask here for advices. E.g., I'd like to know if semicategories have been previously considered by anyone with regard to the definition of a semantics for (finitary) first-order logics. But my concerns are even more primitive, let's say, and this is why I'm looking for a systematic development of the theory from the very basics. – Salvo Tringali Sep 11 at 13:01
	Look at the appendix to the paper Categories as Algebra by Bret Tilson, although it may not be what you are looking for. – Benjamin Steinberg Sep 11 at 13:53
	By the way, until a semigroup is renamed a semi-monoid, I think semigroupoid is a better name than semi-category. There are two good reasons for this. 1) The notion of semigroupoid weakens the axioms of groupoid in the same way that semigroup weakens that of group. 2) Semigroupoid is a multiobject version of a semigroup, rather than a deficient category. – Benjamin Steinberg Sep 11 at 13:55
	Of course, I am not in favor of the name monoidoid, although logical, for categories! – Benjamin Steinberg Sep 11 at 13:56

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References for semicategories

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