Talk:Pushout (category theory)

Untitled
Fropuff: Thanks for your edits, especially the diagrams! The organization is also an improvement. Much appreciated!

Alodyne 20:30, 24 Mar 2005 (UTC)


 * I had been meaning to do the diagrams and expand this article for awhile. Your recent edit prompted me. -- Fropuff 23:37, 2005 Mar 24 (UTC)

Notation
Is there a standard notation for pushout? — Preceding unsigned comment added by Tosha (talk • contribs) 19:02, 15 April 2010

Diagram orientation
The current diagrams must be read from bottom to top and from right to left, i.e. backwards. Wouldn't it be better to switch the positions of P and Z so that P is at the lower right (and move Q accordingly)? -- 92.226.209.41 (talk) 12:05, 19 July 2011 (UTC)


 * I agree with this. Does anybody prefer the current orientation? 2601:644:400:8430:38E5:6E3F:1923:FBC8 (talk) 19:32, 2 March 2024 (UTC)

Standard Notation(s)
In (I think not just) my opinion a standard notation for pushouts should be derived from two ingrediens:

1. the standard notation for coproducts (as main symbol), mostly derived from the symbol for product,

2. the standard notation for pullbacks (indexing).

This leads to the probably most common infix-notation A ⊔B C  formed by an upside-down greek capital letter Pi (Π) indexed by the "intersection" B of the span A←B→C, in cases where the projections are clear. As a reference see Saunders Mac Lane: "Categories for the Working Mathemetician, 2nd Edition", Springer, p.66.

Also valid may be symbols derived from the + sign (for sum = coproduct), or from the symbol (cup) for the union of two sets. More generally, the notation for colimits may be used.

But be aware, that the symbol just refers to the vertex of the pushout! The complete pushout is symbolized by the diagram. — Preceding unsigned comment added by 217.246.176.55 (talk) 11:07, 16 March 2012 (UTC)