Talk:Groupoid

message: I changed the sec head 'Categorical definition' to 'Category theory definition'
to avoid the possible (albeit unlikely) chance of confusion with the term 'categorical' as it is meant in model theory.  'Category theoretical' seemed too awkward.  Of course an argument could be made that the possibility of confusion is so remote as to make my edit unnecessary; Zero sharp 14:54, 21 June 2007 (UTC)
thread_title: Categorical -> Category Theory

message: I don't see how one can derive from the given axioms that if a*b and b*c are defined, then (a*b)*c is. I think one should add this axiom, or explain why it is a consequence of the others.
Also, it is not clear what the "uniquely" in the identity axiom means.
64.81.240.241 (talk) 10:16, 19 November 2007 (UTC)
thread_title:  Problem in the algebraic definition ? 

message: :Any additional comments:
*That discussion is 3 years old??? There's no way it can be used to support a requested move. Please state your reasoning. 76.66.194.183 (talk) 01:00, 19 October 2009 (UTC)
replies: text: The start of it was 3 years old.  But there's more recent stuff further down.  Basically, I want a disambiguation page.  "Groupoid" is also used for a set with a single binary operation.  I dispute that the category-theoretic meaning of the word used on this page is the primary one.  DavidHobby (talk) 03:26, 19 October 2009 (UTC)
replies: text: We do not create disambiguation pages for titles covering only two pages; a hatnote sufficies.  Skomorokh, barbarian  11:09, 27 October 2009 (UTC)

text: The above discussion is preserved as an archive of a requested move.  Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.</div>
I cannot resist observing that the statement "We do not create disambiguation pages for titles covering only two pages" is false in general; as the linked policy page states, when neither topic is primary a disambiguation page is considered the correct thing.  It is debated whether such is the case here, though I see little evidence that those who feel, as I do, that the topic covered by this article is the primary sense of "groupoid" are willing to insist upon this.  Archelon (talk) 03:09, 28 May 2015 (UTC)

text: Hi.  Still watching the article, still want a disambiguation page.  But it seems I never get around to doing it, because it seems like a project. DavidHobby (talk) 10:46, 28 May 2015 (UTC)
thread_title: Discussion

message: Towards the end of the article it mentions that in writing a groupoid as a product $G \times X$ where $G$ is a group and $X$ is a set ($X$ a groupoid with one morphism between any two objects) some information is lost. Is there a way to be more quantitative -- perhaps an example where this is relevant? 
A related question, would it be possible to mention the relationship between the classifying space of a groupoid and that of its maximal subgroup?
Rybu (talk) 13:24, 5 October 2010 (UTC)
thread_title:  Groupoids vs. groups 

message: The lead section said:
:In mathematics, especially in category theory and homotopy theory, a groupoid (less often Brandt groupoid or virtual group) generalises the notion of group and of category in several equivalent ways.
and then went on to define a groupoid as a type of category. A "generalisation of the notion of category" would entail that a groupoid is not necessarily a category, which is incorrect. (To compare the group-theoretic definition, a group is a groupoid whose operation happens to be total, but a groupoid whose operation is properly partial is not a group.) So I removed the phrase "and of category". Hairy Dude (talk) 23:26, 13 October 2010 (UTC)
thread_title:  Not a generalisation of categories 

message: "For elements x and y of X, let the set of morphisms from x to y be G. Composition of morphisms is the group operation of G."
Those morphisms will have no composition (unless x=y)!
77.125.6.136 (talk) 07:55, 18 August 2012 (UTC)
thread_title:  Composition? 

message: "Heinrich Brandt introduced groupoids implicitly via Brandt semigroups in 1926" is most probably false. See Clifford, Preston "The Algebraic Theory of Semigroups" vol. 1.  — Preceding unsigned comment added by 178.36.13.246 (talk) 03:20, 5 April 2013 (UTC)
thread_title:  Brandt 

message: It looks weird using the $\exists$ symbol for an expression.  It's fine saying $a^{-1} * a$ exists, although maybe is defined is better, but using the symbol that way gets strange.  — Preceding unsigned comment added by 31.52.247.252 (talk) 17:45, 7 April 2013 (UTC)
thread_title: Exists symbol

message: Could someone please explain what are the natural equivalences of morphisms.
Could someone please explain what is meant by conjugacies of morphisms.
If Grpd is the category of groupoids, and G and H are two groupoids,
what is Grpd(G, H)?  Howard McCay (talk) 20:54, 4 January 2014 (UTC)
thread_title: Category of groupoids

message: It would help if the first example, "Linear algebra" were easier to understand. I think I can follow the first two sentences: they are saying that union of the groups GL(n,k), where k is a specified field and n ranges over all positive integers, forms a groupoid. The third sentence uses the undefined term G0, making it hard to understand. Similarly, the fourth sentence uses the undefined term G(m,n). Maproom (talk) 09:24, 14 May 2014 (UTC)
thread_title:  Examples 

message: So this edit has moved the article to Groupoid (category theory) (a rather ungainly title in my opinion, but let us leave that aside for the moment) and left Groupoid a redirect to this article (i.e. ). This is of course not a proper state for things to be left in. But I don't feel like writing a disambiguation page to occupy the Groupoid space and fixing all the broken links that would result; that would have been the responsibility of the editor who performed the move, anyway. So I'm moving the page back. This is not because I insist that the category-theoretic meaning of "groupoid" is the primary one (although I admit that is my own preference). Archelon (talk) 03:37, 28 May 2015 (UTC)
thread_title:  Reverted move 

message: Hello fellow Wikipedians,
I have just modified 2 external links on Groupoid. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
*Added  tag to http://www.bangor.ac.uk/r.brown/groupoidsurvey.pdf
*Added archive https://archive.is/20120723235509/http://www.bangor.ac.uk/r.brown/hdaweb2.htm to http://www.bangor.ac.uk/r.brown/hdaweb2.htm
*Added  tag to http://www.cup.cam.ac.uk/catalogue/catalogue.asp?isbn=9780521803090
*Added archive https://web.archive.org/web/20050310034123/http://www.shef.ac.uk/~pm1kchm/gt.html to http://www.shef.ac.uk/~pm1kchm/gt.html
When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.
Cheers.—InternetArchiveBot (Report bug) 14:10, 24 October 2017 (UTC)
thread_title:  External links modified 

message: In the section on comparing the definitions it's stated that the algebraic and category theoretic definitions are equivalent and two constructions are given, one to produce an algebraic groupoid from a category theoretic groupoid, and one to produce a category theoretic groupoid from an algebraic groupoid.  These two constructions are clearly not inverse to each other.  Starting with an algebraic groupoid G, constructing a category theoretic one, and then from that constructing another algebraic groupoid G' one can get that G and G' have different cardinalities, so may not be isomorphic.  In what sense then are we saying that the two definitions are equivalent? 2601:144:C004:1590:44EE:DDE5:D556:DE (talk) 22:51, 13 January 2018 (UTC)
thread_title:  Equivalence 

message: I'm not an expert on groupoids (hence I'm not making an edit just yet), but in "identity", it is said that "If a*b is defined, then a*b^{-1}*b = a, and a^{-1} * a* b = b."
Should this perhaps be "... then a*b*b^{-1} = a, and ..." ?  — Preceding unsigned comment added by 2A02:2C40:2E0:0:590B:B35A:9621:172F (talk) 07:57, 26 March 2018 (UTC)
thread_title:  Algebraic definition of groupoid - mistake in identity? 

message: An editor has asked for a discussion to address the redirect General linear groupoid. Please participate in the redirect discussion if you wish to do so.  –Deacon Vorbis (carbon • videos) 19:08, 25 December 2019 (UTC)
thread_title:  "General linear groupoid" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]] 

message: The category definition ends with this: "and the two arrows G_1 \to G_0 represent the source and the target."  Can that be right?  I don't think it is meaningful.  G_1 is the set of morphisms and G_0 is the set of objects; there is no mapping from the one to the other.  Neither is a source nor a target.  Should this be removed? Zaslav (talk) 05:03, 16 January 2024 (UTC)
thread_title:  Confusion in category definition