Talk:Inverse limit

message: The intro paragraph introduces the term "injective limit" for the direct limit. Is this terminology standard? I have not heard of it. My guess is that the author mixed up injective and *inductive*.
Link to the edit which added the claim. I will replace injective by inductive unless somebody comes up with a source for 'injective.'
https://en.wikipedia.org/w/index.php?title=Inverse_limit&diff=prev&oldid=1049708539
  — Preceding unsigned comment added by 100.34.251.31 (talk) 19:05, 29 August 2022 (UTC)
thread_title: Terminology source?

message: I think that this article has changed for the worse. The version of 14 September 2020 was, for example, much clearer and more to the point.
The definition now given is overtly complicated. The point seems to be lost by introducing many different notations. I think the article should be more closely written to how limits are actually used by mathematicians in practice. 
I advice to write the definition short and succinct, using the full language of category theory, and then offering an unpacking paragraph for the interested reader.  — Preceding unsigned comment added by 85.230.178.159 (talk) 15:57, 10 June 2021 (UTC)
thread_title: Decreased clarity

message: I'm a little lost on the Formal Definition. Theres 7 different 'i's. Which 'i's are bounded to which expressions? Could someone perhaps use a different letter for different expressions?  —Preceding unsigned comment added by 68.81.242.10 (talk) 18:56, 7 October 2010 (UTC)
replies: text: I've had a go at clarifying this. Is it better now? maybe some editors think it is now too fussy. ComputScientist (talk) 19:07, 7 October 2010 (UTC)
thread_title: Lost

message: The article says "Unlike for algebraic objects, the inverse limit might not exist in an arbitrary category." This can give the impression that inverse limits always exist in a category of algebraic objects. I don't know to which extent this is true, but here is a counterexample if the poset is not required to be directed : let I = {a, b} be a set with two distinct elements, ordered by equality (thus not directed); let Ka a field with 2 elements, let Kb a field with 3 elements. The (only) corresponding projective system has no inverse limit in the category of fields, because there would then exist field homomorphisms from the limit field to Ka and to Kb, which is impossible since field homomorphims are injective. Additionnally, if the poset I is empty, the inverse limit doesn't exist in the category of fields, since there are no final objects in this category. Marvoir (talk) 07:58, 7 October 2012 (UTC)
thread_title:  "Unlike for algebraic objects, the inverse limit might not exist in an arbitrary category." 

message: Morphisms in C^I are not defined in the article. Is it a full subcategory? Or are the morphisms homomorphisms that commute with the transition maps?
Surely the short exact sequence must have something to do with the structure of the transition maps?! 129.215.104.100 (talk) 13:54, 26 April 2013 (UTC)
thread_title:  "Short exact sequence of inverse systems" 

message: The article at the present states that the inverse limit amounts to a glue together operation. Perhaps some people can feel this way. I worked (did research) with inverse limits quite a bit, and my intuition is just the opposite: the inverse limit, when projections are surjections or epimorphisms (a typical case), is a result of gradual ungluing consecutive spaces--the approximating spaces are glued in themselves, but less and less so in the limit. When projections are not onto then a different intuition applies; in particular the intersection is a special case of an inverse limit. Once again, there is no gluing here, not at all. Wlod (talk)  —Preceding undated comment added 08:40, 16 May 2013 (UTC)
thread_title:  Gluing or ungluing? 

message: The following page Inverse system also deals with Inverse System, in the language of categories and functors. Maybe it could be integrated as a part of this page ? At least, link between them are needed.
--Tilwen (talk) 13:52, 9 December 2015 (UTC)
thread_title:  Two redundant pages, merging needed ? 

message: The third item in the list of examples, about the groups \mathbb{Z}/p^n\mathbb{Z} and the homomorphisms \mathbb{Z}/p^n\mathbb{Z} \rightarrow \mathbb{Z}/p^{n+1}\mathbb{Z} induced by multiplication by p is a direct system and not an inverse system, with a resulting direct limit instead of inverse limit.  The same example is already present in the Prüfer group and Direct limit articles and should be removed from the current article.  If people agree, I can remove it.  (I know every direct limit is an inverse limit in the opposite category, but that's not useful here.)
Furthermore, for my own benefit, I think the direct limit would be the Prüfer group, and not the circle group \mathbb{R}/\mathbb{Z} as stated.  Would you agree? PatrickR2 (talk) 05:59, 8 August 2021 (UTC)
replies: text: This has now been removed. PatrickR2 (talk) 22:49, 11 August 2021 (UTC)
thread_title:  Prufer group example