Talk:Span (category theory)

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Is there any reason to define span and cospan the way it is done initially in this article, before defining them as "diagrams of the form Y <--- X ---> Z" and "Y ---> X <--- Z"? The latter is the the one that makes sense...why throw in a functor to start off with? I am considering reversing the order in which these two definitions are given in the article...does anyone object? — Preceding unsigned comment added by MorphismOfDoom (talk • contribs) 16:10, 4 May 2017 (UTC)