Talk:Cone (category theory)

Comma category

If Δ : C → C^J but F : J → C, then how does (Δ ↓ F) make sense? The functors for a comma category ought to have the same codomain. Perhaps you need to think of F as a global element 1 → C^J in some category of categories?

> Yes, that is precisely what is meant by this slight abuse of notation: we consider F as functor 1 → C^J, which has the same domain as the diagonal functor. 145.97.196.76 (talk) 20:17, 11 August 2011 (UTC)[reply]

> > I believe this observation should be incorporated into the main text. It is an abuse of notation which should really be explicitly stated. Bruno321 (talk) 19:32, 19 April 2012 (UTC)[reply]

>>> In the book by MacLane, it details four special cases of comma category, where indeed one can have (functor ↓ object). — Preceding unsigned comment added by 192.76.172.10 (talk) 16:23, 14 September 2013 (UTC)[reply]

The definition of cone seems to be equivalent to (N ↓ F) rather then (Δ ↓ F), is there anything missing?

What is 'J'?

This article uses the symbol J without defining it, making it impossible to understand for someone who doesn't already know the content. What is J here, and can we have a link to whatever it is? Nathaniel Virgo (talk) 12:22, 18 November 2017 (UTC)[reply]

Its a small index category. For example, the discrete category with 2 objects in it, or the span (category theory). I'll try to fix the article. 67.198.37.16 (talk) 07:27, 26 February 2018 (UTC)[reply]

Usually infinite?

Why is the collection of triangles "usually infinite"? Plenty of elementary constructions -- kernels, products, whatever -- involve finite collections in their cones.Chan-Paton factor (talk) 18:27, 16 January 2020 (UTC)[reply]