On 09/26/17 9:28 PM, Patrik Eklund wrote:
The category of graphs may also need revision. Defining a graph as mapping an edge to a pair of vertices hides arities and invites to defining paths. Nevertheless, vertices in trees are seen as operator names.
Even though categories are not algebraic in sets, at least they are algebraic in graphs, which in turn are algebraic in sets. While I would have little or no quarrel with any revision of "the" category of graphs that preserved this fundamental relation between categories and sets, if the revision you have in mind does not then I would expect at least some of us here would be very interested in why you consider your contemplated revision an improvement. Vaughan Pratt [For admin and other information see: http://www.mta.ca/~cat-dist/ ]