A couple of days ago the tag appeared. Unfortunately, there are two different definitions of the word "groupoid" coming from category theory and from abstract algebra. When browsing the list of questions currently tagged , one immediately sees that

Any suggestions/ideas on how we deal with this particular set of conflicting terminology?


we could conceivably come up with two separate tags for the two concepts. Or we can have a tag-wiki requesting users to disambiguate by tagging appropriately also or . Other ideas are also welcome.

  • $\begingroup$ What is the status now? Can I continue as I intended or should I wait for further opinions? $\endgroup$ – t.b. Apr 24 '12 at 14:02
  • $\begingroup$ @t.b. since there seem to be little interest, you should go right ahead with the tagging and the writing of the tag wiki. I'm sure the ambiguity will also resolve itself once a tag wiki is available. I'll retag the odd one out to remove the groupoid tag. $\endgroup$ – Willie Wong Apr 24 '12 at 14:06
  • $\begingroup$ Okay, that's what I figured, but I wanted to ask for confirmation. I will do this in the next few days, then. Thanks for the quick reply. $\endgroup$ – t.b. Apr 24 '12 at 14:09

I introduced the tag at the request of the OP of An example of functions on a groupoid (see the revision history, at the very end of the post). The introduction of the tag seemed like a good idea to me (also given that Ronnie Brown has become active here, recently). In that question the context makes it certain that groupoids in the categorical sense are intended. I was going to populate the tag slowly over the next few days. The intention clearly was to cover groupoids in the categorical sense and if nobody objects to this usage of the tag, I will write a tag wiki indicating this intention and the ambiguity.

To be honest, I was completely unaware of the usage of groupoids in the sense of magmas in universal algebra and I'm pretty sure that I haven't ever seen it used anywhere or I probably would have remembered. Thus, I didn't look carefully enough when adding the tag to the odd one out among the three questions you list.

Also, I'm pretty certain that exclusively categorical groupoids are intended whenever the word groupoid is mentioned in algebraic topology, algebraic geometry, differential geometry, mathematical physics, functional analysis, ergodic theory, and of course category theory, see my answer to definition of a groupoid for a small sample of its usage. Compare also Qiaochu's comment to the question that is currently tagged in the universal algebra sense.

Magmas seem too special (or rather too general) to me to merit a separate tag. The should amply suffice for them.


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