Talk:Equaliser (mathematics)

solution

What is a solution set of the equation 3x^2-20x=7

{−1/3, 7}. Why? -- Fropuff 01:06, 7 December 2005 (UTC)

coequalizer

... And without offense to authors, the articleCoequalizer is appealing. It begins in the context of Category Th. whereas Equaliser (mathematics) starts in Set Th.

Does anyone object to a new article Equalizer (mathematics) strictly dual to Coequalizer? When these two articles are "up to snuff" Equaliser can be deleted. Thanks, PeterEasthope 14:09, 27 May 2007 (UTC)

I object. I think for people without background in category theory or who are just learning category theory, explanations starting with the set theoretic notions are much easier to comprehend. Hence, I am in favour of starting with set-theoretic kernels, quotients and such and only later on reveal the categorical background including duality. This also means that the two articles should not be merged into one. Cf. also the paedagogical style of Adamek, Herrlich, Strecker: "Abstract and concrete categories", which is much more readable than the style of MacLane: "Categories for the working mathematician", who that first introduces the most general notions and then specializes them. By the way, AHS have separate sections for equalizers and coequalizers, see p. 114ff. --Tillmo 09:34, 28 May 2007 (UTC)

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Hello Tillmo, I didn't mean to merge the equalizer and coequalizer articles. Keep both. These are my concerns, restated.

1. In the Coequalizer article, the link "equalizer" should lead to an article entitled "Equalizer (mathematics)"---not to a disambiguation.

2. Spelling should be consistent. Either equalizer and coequalizer or equaliser and coequaliser. The OED writes equalizer.

3. The two articles should be duals. No need to tell the reader that. Duality of the articles or absence of it is obvious.

4. We needn't argue about the context of set theory versus cats. There are at least two solutions which both of us might accept. We can upgrade the Coequalizer article on the pattern of the Equalizer. Ie., define in Sets first and then progress to Cats. Alternatively, we can have articles in both contexts. "Equalizer (set theory)", "Coequalizer (set theory)", "Equalizer (category theory)", "Coequalizer (category theory)".

Regards, PeterEasthope 14:33, 11 June 2007 (UTC).

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Naming discussion (May 2007)

The following discussion is closed. Please do not modify it. Subsequent comments should be made in a new section.

Spelling should be consistent: Equalizer and Coequalizer. The OED spells it "equalizer". If I fix this, will anyone object? Thanks, PeterEasthope 03:20, 21 May 2007 (UTC)

No one replied, so I've fixed this. Equalizer is by far the most common spelling. The article needs to swapped with the redirect page Equalizer (mathematics). Any objections to this? Sam Staton 11:20, 30 October 2007 (UTC)

By way of further argument: I think the spelling "equalizer" is the most widespread in mathematical literature. User:Gene Nygaard says this is a potential controversial move (see Wikipedia:Requested_moves) because of [varieties of English]. If anyone really does object to a rename, please say! Sam Staton (talk) 22:42, 20 November 2007 (UTC)

Oh, I didn't think this would be a big issue! Now Dekimasu has reverted my changes through the document, I think on the grounds of consistency within the article. If the article is renamed, that will have to be undone. To clarify, I propose the changes (and am aware of that one should typically retain the existing variety) for the following reasons:

• Consistency with the articles Coequalizer, Limit (category theory), Pullback (category theory)
• Consistency with by far the most common mathematical usage, and in particular the standard text by Mac Lane on the topic.
• On the grounds of Opportunities for commonality: this spelling is the only spelling allowed by either the OED or American English. See also American and British English spelling differences, where it is written "Worldwide, -ize endings prevail in scientific writing and are commonly used by many international organisations [sic!]".

(In case it's relevant: I am British.) Sam Staton (talk) 09:33, 21 November 2007 (UTC)

I'm sorry to have confused you - I wasn't referring to consistency within the article, but to "retaining the existing variety", slightly farther down the page (cf. the description at {{Uw-lang}}). For what it's worth, I use American English. Dekimasuよ! 12:56, 21 November 2007 (UTC)

Here is the text of the original contested request, moved here from WP:RM.

• Equaliser (mathematics) → Equalizer (mathematics) — Spelling in keeping with the article itself —Sam Staton (talk) 19:09, 20 November 2007 (UTC)

Sam Staton changed the spellings in the article. We probably have a real national varieties of English issue here. Gene Nygaard (talk) 21:50, 20 November 2007 (UTC)

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The above discussion is closed. Please do not modify it. Subsequent comments should be made in a new section.

Requested move (December 2007)

The following discussion is an archived discussion of the proposal. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section.

The result of the proposal was no consensus. WP:ENGVAR's "retaining the existing variety" is indeed relevant here. Angus McLellan (Talk) 18:02, 1 December 2007 (UTC)

Equaliser (mathematics) → Equalizer (mathematics) — Creating RMT discussion area on behalf of Sam Staton, who has stated his reasons for supporting a move above. —Dekimasuよ! 13:01, 21 November 2007 (UTC)

Survey

Feel free to state your position on the renaming proposal by beginning a new line in this section with *'''Support''' or *'''Oppose''', then sign your comment with ~~~~. Since polling is not a substitute for discussion, please explain your reasons, taking into account Wikipedia's naming conventions.

• Oppose. As far as I can tell the proposed move violates the WP:ENGVAR section on Retaining the existing variety. – Axman (☏) 06:30, 24 November 2007 (UTC)

• Weakly support. See my reasons above. I now see some people are quite sensitive about all this (though apparently no specialists in the subject); I'm not especially bothered. I maintain that the mismatch between the "equaliser" page and the "coequalizer" page is very ugly and inconsistent. (For those unfamiliar: the concept of coequalizer is dual to equalizer, so the concepts are very intimately connected.) Perhaps I should view this mismatch as a good thing, that helps to make wikipedia more "international". Note also that google returns far more for equalizer "category theory" -wikipedia -equaliser (14100 hits) than for equaliser "category theory" -wikipedia -equalizer (564 hits), so perhaps there is a community issue. Sam Staton (talk) 19:15, 25 November 2007 (UTC)

Hmm. I note that inconsistency between articles is not necessarily grounds for a move; see eg Orange (Colour) and Color. Perhaps the guidelines could be clarified on these points. Sam Staton (talk) 10:00, 28 November 2007 (UTC)

Discussion

Any additional comments:

No vote as yet... it's a hard call IMO. The Google counts are not necessarily representative, as US-published papers and abstracts in mathematics are far more likely to be on the web than those of other English-speaking countries. New Zealand has for example been a hotbed of this area of research from time to time, and many of its alumni still write equaliser on the blackboard. (But of course if they publish in US journals, this is "corrected". Possibly even the US-based abstracts of overseas-published papers are corrected as well, I'd have to check.) Andrewa (talk) 18:33, 26 November 2007 (UTC)

Thanks Andrew, you are right. I am rethinking my vote. The frequency of one spelling could be down to the journal editors. I'm really not sure whether that should be reflected here. By the way, is the "izer" spelling actually considered wrong in New Zealand or Australia? Either is OK in the UK. Sam Staton (talk) 10:00, 28 November 2007 (UTC)

The above discussion is preserved as an archive of the proposal. 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.

Equational definition

Can equalizers be given "Equational definition" (like one in Product_(category_theory))? --VictorPorton (talk) 18:35, 14 October 2013 (UTC)

Hi, Victor, I'll respond to you here after almost two years, since I know that you're still around, and MediaWiki should give you a notice about this (since I linked your user name).

The biggest difference here is that instead of an operation ⟨−, −⟩ (pairing), we have an operation −|^{f=g} (restriction of codomain); and while ⟨f₁, f₂⟩ exists whenever f₁ and f₂ have the same domain, m|^{f=g} only exists when all of these conditions are met:

• f and g have the same domain and the same codomain,
• the codomain of m matches the common domain of f and g, and
• f ∘ m = g ∘ m.

The first two of these are analogous to the requirement for ⟨f₁, f₂⟩, but the last is on a different level logically. That is, we not only require that the variables (in this case m, f, and g) have appropriate types (their domains and codomains) but we also require an equation to hold. (Compare how, in ordinary algebra, x − y exists as soon as x and y share the appropriate type of a real number, while x ÷ y only exists if additionally the inequation y ≠ 0 holds.)

Similarly, there is a bit of material that should come before the stuff at Product_(category_theory)#Equational_definition, and the corresponding material here is a bit more involved. There, we merely need to state that an object X₁ × X₂ (which is confusingly called simply "X" in that part of the article) exists whenever X₁ and X_{2 are objects. Here, we analogously state that a morphism eq(f, g) (which is called simply "eq" in the diagram) exists whenever f and g are morphisms with the same domain and the same codomain. Additionally, we also have to state that the codomain of eq(f, g) matches the common domain of f and g (which is really just a typing declaration) and the equation eq(f, g) ∘ f = eq(f, g) ∘ g (which again is more than a typing declaration).}

With that understood, here's my translation:

• Existence of u (when it exists) is guaranteed by the operation −|^{f=g}; that is, u = m|^{f=g} (if the conditions are met for this to be defined). Here we should also note that the domain of m|^{f=g} is the domain of m, while its codomain is the domain of eq(f, g) (which was written as "E" in the diagram but would more unambiguously be called Eq(f, g)).
• Commutativity of the diagram is guaranteed by the equality eq(f, g) ∘ m|^{f=g} = m (if the same conditions are met).
• Uniqueness of u is guaranteed by the equation (v ∘ eq(f, g))|^{f=g} = v whenever the codomain of v is Eq(f, g) (which is sufficient to guarantee that (v ∘ eq(f, g))|^{f=g} exists).

You might see if Lambek (the citation given in the Product article for this) discusses this as well, so that you could cite it. Or you could always add this to the nLab if you just want to have it somewhere.

—Toby Bartels (talk) 01:10, 27 September 2015 (UTC)

Requested move 19 September 2015

The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review. No further edits should be made to this section.

The result of the move request was: not moved. Clear ENGVAR case. Jenks24 (talk) 15:59, 27 September 2015 (UTC)

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Equaliser (mathematics) → Equalizer (mathematics) – This extends the discussion above from 8 years ago. Use American English, per WP:ENGVAR. GeoffreyT2000 (talk) 01:40, 19 September 2015 (UTC)

• Comment what has changed which you believe makes this worth a third discussion on this topic? Tiggerjay (talk) 18:06, 19 September 2015 (UTC)
• Oppose. WP:ENGVAR spelling issues for article titles are usually determined by an examination of the edit history of the article. The questions of commonality across different varieties of English and consistency across different articles are usually not decisive. That may not be my personal preference for how Wikipedia should work, but it is my personal impression of how it normally actually works, so that is the basis of my expressed opinion. The article started at "Equaliser" on 3 September 2003. Since it was created, the article has not gotten much longer, so we don't need to worry too much about what was the first non-stub version. I believe the biggest addition ever was 345 characters (19:12, 12 January 2011), and that's not a very big edit. The result of that particular edit was not consistent in regard to spelling, although it tilted the article content very slightly toward 'z' spellings (by adding one instance of "equalizer" while leaving alone some other instances of "equaliser"). I thus think the proper basis for determining the variety of English for the article would be the original edits of 3 September 2003 by Toby Bartels. That version was clearly using 's' spellings, not 'z' spellings. It had more than 20 uses of "equaliser" or "generalised", and the only use of "equalizer" was at the beginning as an explanation that such an alternative spelling exists. The article currently uses mostly 'z' spellings, but is not entirely consistent, as it also contains "generalised" and "generalisation". Two previous RM discussions have failed to convince the community that the spelling of the title should be changed. The records of the previous discussions (per a comment by Gene Nygaard) seem to indicate that a single editor (Sam Staton) was primarily responsible for the general drift from 's' to 'z' – the same person who twice suggested renaming the article. That's not how we generally do things around here. That editor seemed to later be open to retaining the current title. Since the original article used 's' spellings consistently, the article should revert to that usage – and thus it should retain its current title. —BarrelProof (talk) 21:36, 19 September 2015 (UTC)
• Oppose per MOS:ENGVAR. Started as Equaliser and the history shows only page move has been to current title Equaliser (mathematics) at this edit [1] to redirect Equaliser to Equalizer. Zarcadia (talk) 11:49, 21 September 2015 (UTC)
• Comment. If I started this article today (instead of in 2003), I would call it Equalizer (mathematics), but I'm not sure that that's relevant. I will try to gather some evidence on the usage of the term in countries like Australia etc. —Toby Bartels (talk) 23:06, 26 September 2015 (UTC)

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RfC: Harmonize spelling with the Coequalizer article?

The following discussion is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

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We have an article about coequalizers, which are dual to equalizers in category theory. But there is currently a spelling variant inconsistency. Should we therefore harmonize the spelling for Equaliser (mathematics) and Coequalizer? If so, then we need to decide whether we should use the British "ise" spelling for both, or the American "ize" spelling for both. On the one hand, if "ise" should be used for both articles, then "Equaliser (mathematics)" should stay at its current spelling and "Coequalizer" should be moved to "Coequaliser". On the other hand, if "ize" should be used for both articles, then "Equaliser (mathematics)" should be moved to "Equalizer (mathematics)" and "Coequalizer" should stay at its current spelling. Merry Christmas and Happy New Year, GeoffreyT2000 (talk) 22:47, 8 December 2018 (UTC)

• British since coequaliser was added in 2003 to Equaliser before the Coequalizer redirect and article was started in 2004. Dicklyon (talk) 23:04, 8 December 2018 (UTC)
• No change needed The unit of spelling consistency is the article. Not even closely related articles need to be written in the same variety. --Trovatore (talk) 00:25, 9 December 2018 (UTC)
• I hate to do this, but: Merge coequalizer here, which I realize isn't what's being asked, but I guess that also would entail leaving the spelling here be. –Deacon Vorbis (carbon • videos) 05:25, 10 December 2018 (UTC)

  I think that's a good idea, too. Dicklyon (talk) 05:42, 10 December 2018 (UTC)

  Hmm, I'm not so sure. It's not my field, but at a glance there seems to be noticeable divergence between the two articles; I suspect their use in practice is rather different. Just because two notions are dual in category-theoretic terms doesn't really make them the same topic — consider direct limits and inverse limits, which have a quite different feel to them.
  In any case, I think that if a merge is to be done, it should be on its own merits; the spelling issue should play no part. The cost of having the two articles written in different varieties should be set at zero. --Trovatore (talk) 02:11, 11 December 2018 (UTC)

  Ehh, yeah. I've been waffling back and forth about this ever since I suggested it. These two articles seem to have developed a bit differently, but they really could be written almost identically, save for the opposite notions everywhere. But, I'm not sure enough it's worth it to really bother I guess. Anyway, yeah, unless there's something we all missed, I don't think the spelling in either place should really change. We live with inconsistent English variety article titles on WP; that's just kind of how it goes. –Deacon Vorbis (carbon • videos) 02:31, 11 December 2018 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

Requested move 25 December 2019

The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion.

The result of the move request was: No consensus.(non-admin closure) Cwmhiraeth (talk) 16:39, 1 January 2020 (UTC)

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Equaliser (mathematics) → Equalizer (mathematics) – Title is in British English while article is in American English. Corresponding article coequalizer also in American English 73.168.5.183 (talk) 22:58, 24 December 2019 (UTC)

This is a contested technical request (permalink). -- /Alex/₂₁ 01:25, 25 December 2019 (UTC)

Although the majority of the article uses AmE spelling, the original version was written completely using BrE. This would probably need a discussion. In fact, there has been twice before apparently, which resulted in a "no consensus" the first time, and a "not moved" more recently. As far as inconsistent titling between equaliser and coequalizer, welcome to Wikipedia . –Deacon Vorbis (carbon • videos) 23:18, 24 December 2019 (UTC)

• Oppose no reason to Americanize. Spelled with s in India. In ictu oculi (talk) 20:52, 26 December 2019 (UTC)
  • Comment The issue is that there is no consistency in the article at all with regards to the spelling. It should either be written in all American English or all British/Comonwealth English, according to the Manual of Style. Currently the article is mostly in American English but the title of the article and one section is in British/Comonwealth English. As such, would you agree that the entire article should be rewritten instead to be in British/Commonwealth English? 73.168.5.183 (talk) 04:42, 27 December 2019 (UTC)
• Comment since I've seen that this has been marked as contested and moved to the talk page, I should think it well to link the Manual of Style section MOS:ARTCON and Wikipedia's articles on title consistency WP:CONSISTENT and WP:TITLECON to this discussion, since I believe both to be pertinent to this discussion. Personally for me, it seems that since the vast majority of both this article itself and the rest of the category theory articles on the English Wikipedia use the American spellings for category theoretic terminology, according to MOS:ARTCON, WP:CONSISTENT, and WP:TITLECON the spellings on this article ought to be Americanised. The proper alternative to the suggested change would be to standardise all category theory articles to the British/Commonwealth spellings, which means moving Coequalizer to Coequaliser and modifying the articles Pushout (category theory), Pullback (category theory), Limit (category theory), Universal property, and so on. 73.168.5.183 (talk) 03:13, 27 December 2019 (UTC)
• Comment 2 I've noticed above people using WP:ENGVAR to justify opposing changing the article's title. However, this article does not satisfy MOS:TIES as it is a maths article, and MOS:RETAIN does not really apply due to the consistency issues mentioned above regarding MOS:ARTCON. MOS:COMMONALITY says 'Use universally accepted terms rather than those less widely distributed, especially in titles'; however, I believe the more universally accepted terms in the mathematics and category theoretic literature and journals are the American spellings, especially as category theory was developed primarily by non-Commonwealth mathematicians such as Alexander Grothendieck, William Lawvere, Saunders Mac Lane, Samuel Eilenberg, and Peter J. Freyd who used either American English or a foreign language, and I believe it still remains true today. One can search on Google Scholar or the arxiv for the terms 'equalizer' vs 'equaliser' to check the veracity or falsehood of my statement. All this and the above comment means that WP:ENGVAR ought to be used in support changing the article's title to American English. 73.168.5.183 (talk) 03:44, 27 December 2019 (UTC)
• Comment 3 The equivalents in signal processing (Equalizer (audio)) and telecommunications (Equalizer (communications)) are also written in American English, despite the fact that many of the reasons to justify keeping the title of this article spelled the British/Commonwealth manner would also apply to switching the titles of those articles over to British/Commonwealth English. In fact, the only argument for keeping the title of this article the way it is right now seems to be for historical reasons mentioned by User:Deacon Vorbis above, which IMHO is a fairly weak argument to the consistency and standardisation arguments not only with the rest of Wikipedia but also with the mathematics literature outside in favour of changing the title. 73.168.5.183 (talk) 04:00, 27 December 2019 (UTC)
• Comment 4 If this is resolved in favour of standardising the article on British/Commonwealth spellings, then one should use Template:Engvar on Template:Category theory for the different spellings of equaliser/equalizer and coequaliser/coequalizer. It may also be necessary to include Template:British English. 73.168.5.183 (talk) 04:56, 27 December 2019 (UTC)
• Oppose move and restore BrE spelling per WP:RETAIN. Although I personally prefer AmE I don't see any strong argument for going against principles just for this one case. —David Eppstein (talk) 06:53, 27 December 2019 (UTC)

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