Talk:Cofibration

message: I have made several major edits. There was at least one substantial error (conflating semisimplicial and simplicial sets), there may be others remaining.  — Preceding unsigned comment added by Gadget142 (talk • contribs) 20:55, 17 June 2023 (UTC)
thread_title: Cleanup

message: I think A must be a subset of X.
- Well then i is simply an inclusion map. It is better in my opinion to consider a mapping cylinder of A ajoined to X instead of just (X x 0) U (A x I).
In the third basic theorem, I don't think the biconditional always holds. I think A may have to be closed for the reverse direction to hold.
A is always closed. Follows from retraction or extension property. We  may need Hausdorff though, but I am pretty certain we do not.  —Preceding unsigned comment added by 128.12.72.244 (talk) 03:26, 2 October 2007 (UTC)
thread_title: Subset

message: I added the compactly generated condition for a cofibration to be closed inclusion. May's book page 42 seems to say this is so, but maybe he means an arbitrary space. I haven't found a proof yet but I'll get back if I do. Money is tight (talk) 15:19, 24 January 2011 (UTC)
replies: text: May prefaces chapter 6 with a reminder that all spaces are to be taken as compactly generated. i.e. A, X, Y. Exactly how this definition might be altered if they are not is not stated.  User:Linas (talk) 01:44, 16 August 2013 (UTC)
thread_title:  Additional condition 

message: The "definition" given in the text (closed inclusion = injective with closed image) is misleading.  The subspace that is included also needs to carry the subspace topology!  I suggest writing "inclusion of a closed subspace" instead of "closed inclusion" to avoid this ambiguity. --134.99.156.114 (talk) 08:01, 6 May 2015 (UTC)
thread_title: Closed inclusion

message: On 02:11, 12 December 2015‎ User:TakuyaMurata proposed that this article, and the Homotopy extension property be merged, but did not provide a reason.  Discuss below.
* Don't merge. These are clearly different topics, despite the fact that they are often discussed together. Merging would just confuse the discussion. 67.198.37.16 (talk) 06:20, 5 September 2016 (UTC)
replies: text: Yes, well, I understand that. But I think its OK to have multiple smaller articles with overlapping, duplicated content, rather than one big, one-size-fits-all article. I have a lot of trouble reading big long articles, my eyes glaze over; they are daunting. Short articles are just easy-pickins. As User::Ronnie Brown points out, there is certainly a lot more that can be said about either topic; it would be best if all these articles used the same notation, at least, that is more important. 67.198.37.16 (talk) 09:04, 24 October 2016 (UTC)
replies: text: If the discussion becomes substantial, we can always break up the article. There are advantages and disadvantages for having separate articles on closely connected topics. Right now, the most unfortunate drawback is that the readers are being required to read the "homotopy lifting" article unless he is already familiar with the concept of cofibration and homotopy lifting. One constant criticism on math articles in Wikipedia is that they are (or seem to be) written for those who already know the definition as well as the applications. I think this article is a good example of this. The cheapest solution is to simply merge the two articles. Anyway, this is just a proposal and I don't insist on the implementation. -- Taku (talk) 06:23, 29 October 2016 (UTC)
thread_title:  Merge proposal