Talk:Diagram (category theory)
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Variance of a diagram
[edit]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:C→D to mean F:Cop→D. 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)
Accessibility
[edit]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)