Talk:Diagram (category theory)

From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
WikiProject Mathematics (Rated Start-class, Mid-importance)
WikiProject Mathematics
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
Start Class
Mid Importance
 Field:  Foundations, logic, and set theory

Variance of a diagram

Is a "functor" here necessarily a covariant functor? Stephan Spahn (talk) 20:06, 28 May 2011 (UTC)

Hi Stephan, this is a strange question. A functor is a functor. To say "a contravariant functor from C to D" is an elaborate way to say "a functor from Cop to D". Nobody should ever use the notation F:CD to mean F:CopD. Occasionally someone might use the phrase "covariant functor" if they want to emphasize the point, but it is not necessary to say covariant at all.
I don't think that your addition of (covariant) is necessary here, but we can leave it for a few days in case anyone else has a strong opinion. ComputScientist (talk) 10:16, 30 May 2011 (UTC)
You are right, its not really 'necessary', and its even vaguely awkward, but ... if you are reading this for the first time, and trying to set this in your head, a valid question would be: "gee, do they mean any functor, or just the covariant ones?" and so adding that qualification is appropriate: it promptly eliminates one bit of loose footing. As loose footing is one reason I stumble, I'd say 'keep it'. linas (talk) 15:42, 13 August 2012 (UTC)


The article would be more accessible to interested amateurs if it offered some motivations or intuitions for the notions of "diagram" and "cone". I'm not asking for the historical reasons for these terms, just an indication of why these terms might suggest themselves for, or partly describe, the relevant notions of category theory. yoyo (talk) 22:13, 23 December 2011 (UTC)

Is saying that "its like an indexed family in set theory" not enough? Perhaps its not. The examples could be expanded to mention products, coproducts, pullbacks pushouts and limits; would this be enough? linas (talk) 15:38, 13 August 2012 (UTC)
Retrieved from ""
This content was retrieved from Wikipedia :
This page is based on the copyrighted Wikipedia article "Talk:Diagram (category theory)"; it is used under the Creative Commons Attribution-ShareAlike 3.0 Unported License (CC-BY-SA). You may redistribute it, verbatim or modified, providing that you comply with the terms of the CC-BY-SA