The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.

The result was Keep. Tim Vickers (talk) 00:32, 1 May 2008 (UTC)[reply]

Induced homomorphism[edit]

Induced homomorphism (edit | talk | history | protect | delete | links | watch | logs | views) (delete) – (View log)

Contested PROD; tag removed by an uninvolved editor on the basis that it is a relevant mathematical subject. However, as written the article is purely a short explanation followed by an exercise for the reader - Wikipedia is not a textbook. The short explanation should instead be included in Homomorphism. Ros0709 (talk) 11:51, 20 April 2008 (UTC)[reply]

• Merge with Homomorphism not notable enough to have own article, per nom.  Atyndall93 | talk  13:41, 20 April 2008 (UTC)[reply]
• Comment. I cleaned up the article and marked it as a stub. Homomorphism is the wrong target for a merge; group homomorphism would be better, but still is much less about topology than this article is. The place where this subject is actually discussed is Fundamental group#Functoriality. I'm not yet sure whether a separate article on this subject is worth keeping or not, but if not, I think the redirect should go to fundamental group. If it is kept, we should add a "main article" link to the Functoriality section and merge some of the material from there into this article; the fact that some other sections of fundamental group already have their own main article links suggests that it was already thought to be a good idea to split the Wikipedia material about fundamental groups into smaller articles, which lends support for keeping this one. —David Eppstein (talk) 18:29, 20 April 2008 (UTC)[reply]
• Delete or at least make a disambiguation page. I agree with the first part of Eppstein's comment that homomorphism and group homomorphisms are the wrong merge targets, and that the obvious choice is a merge with the fundamental group article. I disagree with the second part: there can be many different kinds of induced homomorphism. In fact, any kind of functor (into the category of groups, rings, etc.) is going to give "induced homomorphisms". The article as it stands is a perversely narrow use of the word. At best, if this survives, it should be a disambiguation page indicating the various kinds of induced homomorphisms available. Redirection would serve no encyclopedically useful purpose. silly rabbit (talk) 18:51, 20 April 2008 (UTC)[reply]
• Do not merge with homomorphism". Look: There's an article titled House numbering. "House numbering is the system of giving a unique number to each building in a street or area[...]" etc. Now suppose it is decided that's not worth an article and it should be merged into something else. What to merge it into? Well, number, of course. Right? How about squad number? "In team sports, the squad number, shirt number, jersey number, sweater number, or uniform number is the number worn on a player's uniform." What to merge it into? Number, of course!! Not something about sports. What about letter bomb? If it needs to get redirected, don't redirect it to bomb; redirect it to letter. Or varsity letter? No, don't redirect to something about college sports; redirect it to letter.

This article is about algebraic topology. If it's not worth an article, it should redirect to a broader article on algebraic topology.

But I'm inclined to agree that it should either be made a disambiguation page or made into a discussion of the general concept with mention of various concrete examples including the one that the article is now about. Michael Hardy (talk) 05:09, 21 April 2008 (UTC)[reply]

• Merge. I'm not sure what that target should be though... maybe I shouldn't be even saying "merge" then. Closing admin: I actually don't know what I'm talking about here probably, but it just seems like a good candidate for a merge to something else. Sancho 16:56, 23 April 2008 (UTC)[reply]

• Delete per silly rabbit above. induced homomorphisms happen everywhere and each instance can be easily treated in the relevant context. having an article on one particular instance is pointless. Mct mht (talk) 08:48, 25 April 2008 (UTC)[reply]

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Relisted to generate a more thorough discussion so that consensus may be reached.
Please add new comments below this notice. Thanks, Sandstein (talk) 06:36, 26 April 2008 (UTC)[reply]

• Note: This debate has been included in the list of Science-related deletion discussions. -- Iain99^{Balderdash and piffle} 09:56, 26 April 2008 (UTC)[reply]

• Merge, probably to Fundamental group. Klausness (talk) 12:20, 26 April 2008 (UTC)[reply]
  • Keep, based on David Eppstein's improvements to the article. Klausness (talk) 18:17, 30 April 2008 (UTC)[reply]

• Merge to the Fundamental group. Merging to homomorphism is not appropriate, since "induced homomorphism" is primarily a topological notion while "homomorphism" refers to a general algebraic term. I do not see sufficient need for keeping a separate article about induced homomorphism. Nsk92 (talk)

Keep and expand per Mct_mht's comments below. Mct_mht and Silly Rabbit are quite right that the term "induced homomorphism" is used in many more situations than just for the maps between the fundamental groups, such as the maps between homotopy, homology and cohomology groups. So it does make sense to keep the article and expand it to include these additional uses. An alternative solution, to prevent problems with redirects, might be to first move the article to something like "Induced homomorphism (fundamental group)" and then merge that with Fundamental group. But keeping and expanding seems better to me. Nsk92 (talk) 09:24, 27 April 2008 (UTC)[reply]

• Do not merge with Fundamental group. if i understand correctly, merging includes making this a redirect to it. as silly rabbit pointed out above, there are all kinds of induced homomorphisms, in homology, in K-theory... the list goes on. redirect to a particular context is a bad idea. Mct mht (talk) 21:13, 26 April 2008 (UTC)[reply]

Fair enough. I was trying to come up with something more specific than Algebraic Topology, but perhaps that's the best we can do. Klausness (talk) 21:29, 26 April 2008 (UTC)[reply]

• Keep. Per Silly Rabbit, induced homomorphisms abound, to my mind this makes the concept worthy of an article. For some basic references see for example: [1], [2], [3], [4], [5]. Paul August ☎ 04:25, 27 April 2008 (UTC)[reply]

These precisely indicate that we should not keep this article. Notice that all but two of the meanings are different in these different places and the two that are the same are not the same as the one discussed in induced homomorphism. There is no way to cover all these instances. If you search for example for induced topology, you will also find many hits. Do we want an article called induced topology? I hope not. What about induced order? Should we have an article fresh milk and an article spoiled milk? Oded (talk) 15:30, 30 April 2008 (UTC)[reply]

• Merge and redirect, if and only if knowledgeable editors can identify an appropriate location. In the future, try just doing a merge/redirect yourself. Since this is a valid term that deserves at section in some other article, putting it up for deletion is obviously the wrong solution. And if there's no good place to merge/redirect to, then apparently the concept needs to stand on its own, so keep. -- SCZenz (talk) 07:29, 27 April 2008 (UTC)[reply]
  • This content already has a section in another article: it's described better at Fundamental group#Functoriality than it is in the nominated article. The question is not how to find a better home for the content, it's whether this name is an appropriate one for the content. Although I suggested a merge above, I'm finding myself now more in agreement with the others who say that it's the wrong name (because so many other unrelated concepts could also be called an induced homomorphism) and therefore that the article in its present form should be deleted. If it is deleted, it's no big loss to the project, because as I said the same material is already covered elsewhere. —David Eppstein (talk) 01:41, 28 April 2008 (UTC)[reply]

    If it's one name for lots of content, then make it a disambiguation page. In any case, this deletion discussion is completely moot. Whether the page is deleted or not, somebody should (and hopefully will) come back at a future time and do the sensible thing with this page—and I doubt very much that that's having nothing at the name at all. -- SCZenz (talk) 05:31, 28 April 2008 (UTC)[reply]

• Delete. What is an induced homomorphism? All it is is a homomorphism which is induced. The homomorphism could be a group homomorphism, or a graph homomorphism or any number of other homomorphisms, and it can be induced in many different ways. Having an article by that name serves no useful purpose. It is reasonable that there would be an induce (mathematics) redirect to functor. The content of the present article already appears in all the right places. Oded (talk) 14:31, 30 April 2008 (UTC) [reply]

  Don't you think it's possible that someone will actually look for an article named induced homomorphism? Shouldn't they get some kind of pointer in the right direction? -- SCZenz (talk) 15:36, 30 April 2008 (UTC)[reply]

  Sure, it is very likely that someone will search for induced homomorphism. But we cannot point them in the right direction, because we don't know what that direction is. If there is no page by that name, what happens? They get the list of pages where induced homomorphism appears. Isn't that practically the best that we can do? Right away they see that there are many different induced homomorphisms, and that they should figure out from the context what this means. Oded (talk) 16:09, 30 April 2008 (UTC)[reply]

  That supposes that a text search of Wikipedia is as good as a well-crafted disambiguation page. -- SCZenz (talk) 17:17, 30 April 2008 (UTC)[reply]

  In view of David Eppstein's revision, I change my mind. It is now better than nothing. Oded (talk) 18:26, 30 April 2008 (UTC)[reply]

• Delete. Include in mathematical jargon.--CSTAR (talk) 16:52, 30 April 2008 (UTC)[reply]

Keep. It's definitely better now.--CSTAR (talk) 18:32, 30 April 2008 (UTC)[reply]

• Comment. I rewrote the article from a significantly more general perspective. I think many of the previous comments, regarding an earlier version of the article, do not apply to it in this rewritten form. —David Eppstein (talk) 17:42, 30 April 2008 (UTC)[reply]
  • That's definitely an improvement. Thanks. Klausness (talk) 18:17, 30 April 2008 (UTC)[reply]

    Agree! Oded (talk) 18:26, 30 April 2008 (UTC)[reply]

• Keep. Thanks to David Eppstein for expanding the article. It still needs work, but I think in its current form the scope is both notable and easily addressed in an encyclopedia article. JackSchmidt (talk) 20:01, 30 April 2008 (UTC)[reply]

• Keep per JackSchmidt, OdedSchramm. Nice work David! I recommend a speedy close and keep. This AfD is far too convoluted, and my sense is that the consensus among the "experts" is to close as keep. Recent edits to the article have improved it dramatically. silly rabbit (talk) 20:38, 30 April 2008 (UTC)[reply]

• Comment This is no longer anything like the article I nominated for deletion. Many of the comments, including my own, no longer apply. We should not second-guess whether the contributors of those early comments still hold the same view, and simply speedily close this. It can always be renominated if there is strong feeling by anyone that the article should be deleted, but it appears to me there is a sufficient turn of opinion in favour of closing as keep anyhow. Ros0709 (talk) 21:45, 30 April 2008 (UTC)[reply]

The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.