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What is a solution set of the equation 3x^2-20x=7
... 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)
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).
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)
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:
(In case it's relevant: I am British.) Sam Staton ( talk) 09:33, 21 November 2007 (UTC)
Here is the text of the original contested request, moved here from WP:RM.
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)
*'''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.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)
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:
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 X2 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:
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)
The result of the move request was: not moved. Clear ENGVAR case. Jenks24 ( talk) 15:59, 27 September 2015 (UTC)
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)
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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.
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)
The result of the move request was: No consensus.( non-admin closure) Cwmhiraeth ( talk) 16:39, 1 January 2020 (UTC)
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 article is written in American English, which has its own spelling conventions (color, defense, traveled) and some terms that are used in it may be different or absent from other varieties of English. According to the relevant style guide, this should not be changed without broad consensus. |
This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
What is a solution set of the equation 3x^2-20x=7
... 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)
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).
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)
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:
(In case it's relevant: I am British.) Sam Staton ( talk) 09:33, 21 November 2007 (UTC)
Here is the text of the original contested request, moved here from WP:RM.
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)
*'''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.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)
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:
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 X2 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:
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)
The result of the move request was: not moved. Clear ENGVAR case. Jenks24 ( talk) 15:59, 27 September 2015 (UTC)
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)
Hello fellow Wikipedians,
I have just modified one external link on Equaliser (mathematics). 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:
When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.
This message was posted before February 2018.
After February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than
regular verification using the archive tool instructions below. Editors
have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the
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source check}}
(last update: 18 January 2022).
Cheers.— InternetArchiveBot ( Report bug) 03:56, 22 September 2017 (UTC)
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.
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)
The result of the move request was: No consensus.( non-admin closure) Cwmhiraeth ( talk) 16:39, 1 January 2020 (UTC)
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)