Talk:Nerve (category theory)

html
First: hope I didn't step on anyone's toes by changing the inline TeX to HTML. Second: I don't know why the final image refuses to show up. I have uploaded it twice; it's called Mappings-as-moduli.png. Anyone know what's wrong?

Dave Rosoff 21:53, 23 May 2006 (UTC)

Page Title
Is there any reason why this is Nerve (category theory) instead of Nerve (mathematics)? --Ecpeterson 23:39, 25 September 2007 (UTC)

Definition of simplicial sets
In the recalled definition of simplicial sets, shouldn't Δ be the category of non-empty totally ordered finite sets? Hugo Herbelin (talk) 22:48, 24 October 2012 (UTC)
 * Does it matter? User:Linas (talk) 16:43, 19 November 2013 (UTC)

Intro
FWIW, has a rather more accessible intro; it would be beneficial to have that here too. User:Linas (talk) 16:43, 19 November 2013 (UTC)

absurd intro
I found this to be the first sentence in the article:
 * In category theory, the nerve N(C) of a small category C is a simplicial set constructed from the objects and morphisms of C.

That is absurd. It does nothing to attempt to inform the lay reader that mathematics is what the article is about. I changed it to this:
 * In category theory, a discipline within mathematics, the nerve N(C) of a small category C is a simplicial set constructed from the objects and morphisms of C.

Michael Hardy (talk) 20:27, 23 February 2014 (UTC)

Nerve of a Cover
The nerve of a cover is probably encountered by most people before the categorical abstraction, so it is good to have this example detailed as a particular case of the definition described here for small categories. However, the brief description does not appear to be correct: We can have a finite open cover in which no set is included in another in the cover, but the nerve is connected. This contradicts the description given. Yasmar (talk) 20:49, 16 July 2014 (UTC)