On Mon, Apr 29, 2013 at 11:38:38AM +0000, Simon King wrote:
> Second question: How do we call this structure? It is not a monoid, unless
> there is a single vertex (it has idempotents corresponding to its vertices),
> If it has more than one vertex, then it contains a zero element that one
> obtains when concatenating paths that do not match.
> 
> Florent suggested to call it "monoidoid". 

I think Florent just invented a new name for 'category', or more exactly the
path algebra of a category.
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