Talk:Category of magmas

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What is the precise relationship between a magma and a groupoid? Is magma just a synonym for groupoid, or is there some difference between the two? Revolver 01:42, 16 Mar 2004 (UTC)

A magma is a set with a binary operation defined on the set. The operation need not have identity, inverse, or be associative. A groupoid is a set for which there is no operation defined on the whole set. There is a product only between certain privileged pairs of elements. When that product does make sense, the operation has identity, inverse, and is associative. Thus, a magma and a groupoid are about as different as they can be, although some people call magmas groupoids, which may have been the source of your confusion. I don't think I can describe succinctly the precise relationship between a groupoid and a magma; neither is a special case or generalization of the other. I'm having trouble even thinking of some superstructure that they are both special cases of. A groupoid can be defined as a special kind of a category, whereas a magma cannot (as far as I can see. composition in categories is always associative). None of this applies of course to the unrelated use of the word groupoid to mean magma. In that usage, they are the same. -Lethe | Talk 18:17, 13 November 2005 (UTC)
I think historically magmas were called groupoids by some people, but then the category theory definition of groupoid came into vogue so people needed a name for the old groupoids, hence magma. Besides, magma is a very cool name for such "primordial" objects. I remember wondering as an undergraduate how many axioms one could throw out and still have interesting mathematics. :-) - Gauge 00:55, 7 July 2006 (UTC)