Talk:Limit (category theory)

message: I'm wondering if it would be better to separate out the stuff on colimits.  In fact I've already started a colimit page.  That way there would be more space to discuss the special cases such as products, equalisers and pushouts (and their duals on the colimit) page. Magnus 17:50 Apr 16, 2003 (UTC)
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I think this article needs examples and motivations for the definitions instead of simply giving them out of the blue. Phys 18:08, 1 Sep 2003 (UTC)
thread_title: Untitled

message: Is there a way that you can interpret the limit of a sequence in a topological space as a limit of some appropriate functor between some categories? -Lethe | Talk 23:16, 8 October 2005 (UTC)
thread_title:  limits in [[topology]] versus limits in [[category theory]] 

message: Did you know cone may be views as natural transformations. It could be quite cool to explain limits with that point of view ? -David 12/02/2006
:I've been meaning to incorporate that. I had stated some (minimal) notes at User:Fropuff/Draft 4. There is some more material at Universal morphism#Limits and colimits. -- Fropuff 20:18, 12 February 2006 (UTC)
thread_title: Cones as natural transformations

message: If have encountered in a paper the following definition of creation of limits:
*G is said to create limits for F if whenever (L, φ) is a limit of GF there exists a unique limit (L′, φ′) of F such that G(L′, φ′) = (L, φ).
I consider this to be a rather weird definition of creation of limits, but the author of the paper insists on his definition. Is this definition used in a relevant portion of the literature? --Tillmo (talk) 14:49, 17 January 2008 (UTC)
replies: text: Hi Till. Hmm. It's not Mac Lane's definition, but it's close enough to be confusing! Yes, it would be more tasteful if the author had used a word other than "creates". The most famous theorem about the creation of limits is probably Beck's monadicity theorem, and I guess that would fail for this weaker definition. Sam Staton (talk) 15:15, 17 January 2008 (UTC)

text: In the terminology used in this article G would be said to lift limits uniquely. This is indeed a useful concept, but not the one that is usually meant by create limits. Mac Lane doesn't talk about lifting of limits, only creation. The book by Adámek et. al. discusses both. (Although they use a slightly different definition of creation then that used here—which agrees with Mac Lane. They insist on a unique preimage source not just a unique preimage cone.) Note that creation of limits is equivalent to the unique lifting of limits plus reflection of limits. -- Fropuff (talk) 17:17, 17 January 2008 (UTC)
thread_title: Creation of limits

message: Er ..   I miss something in the definition of a cone, which is allegedly supposed to generalize, among other things, cartesian products (think of J as a two-point discrete category): some property to assure that whenever we have a family (pair) of morphisms from an object in C to the diagram J \subset C (for simplicity), these factor through the cone N? Or (how) can one derive that from the functoriality of the diagram J -> C? For example, in a cartesian set product N = X \times Y, we want pairs of arrows A -> X, A -> Y to factor through N, so we need a morphism A -> N, but  from this definition I dont see why it should exist. Will learn wiki markup later. Promise. H4nne (talk) 07:51, 30 April 2008 (UTC)
replies: text: Taking J the two-point discrete category, a cone indeed is just a pair of arrows. A universal cone is a cone that factors through each (other) cone. You seem to expect that products = cones, but true is that products = universal cones. --Tillmo (talk) 15:17, 30 April 2008 (UTC)
thread_title:  Definition of a cone seems strange. Please comment. 

message: If the commutative diagram showing the cone is itself a diagram, is that diagram F:J→C, or another diagram in C? ᛭ LokiClock (talk) 21:55, 18 March 2012 (UTC)
replies: text: It's another diagram that contains part of the diagram F. Only part of the diagram F is shown, with nodes labelled FX and FY and the edge Ff. Hope that helps. ComputScientist (talk) 08:48, 20 April 2012 (UTC)
replies: text:  It does. My impression was a diagram doesn't contain the objects of the category, but the index category. So this suggests the reverse, that for an X in F:J→C there's a X' in the picture P:I→C such that P(X')=F(X). Then parts of a diagram are just subgraphs. Is that so? ᛭ LokiClock (talk) 11:15, 22 April 2012 (UTC)
thread_title:  Which diagram is depicted? 

message: I mean, if you use Hom all throughout the article, it gives a wrong impression that categories in some way depend on sets. They don't; and Hom exists only for locally small categories. I'd rather rephrase everyting without using Hom.
Vlad Patryshev (talk) 18:19, 1 June 2012 (UTC)
replies: text: It would be extra complication to add an extra C term to every mention of Hom throughout the article. Is there any general statement about categories made with Hom where it must be a set? ᛭ LokiClock (talk) 05:43, 3 June 2012 (UTC)
thread_title:  Does it have to be, basically, based on Sets? 

message: Right now, in the text it says (L, /varphi) and in the image, it says (L, /phi). Sorry for the LaTex-notation, I don't know how to write greek letters here.
134.76.62.225 (talk) 15:48, 11 March 2013 (UTC)
replies: text: Backslash. Also, see Help:Displaying a formula. ᛭ LokiClock (talk) 18:47, 12 March 2013 (UTC)
thread_title:  Change /varphi to /phi in the definition of the limit of a diagramm? 

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thread_title:  External links modified