epatters
commented
3 years ago A question to get started. I think the current implementation explicitly constructs the comma categories F/d, but perhaps we should be constructing presentations of them instead? As a point of comparison, the cited paper shows how, assuming C, D, and F are finitely presented, to finitely present the collage of F (meaning the collage of the profunctor represented by F). The collage contains essentially the same data as all the comma categories used in the formula for Sigma_F (see Proposition 1 and Lemma 2).
kris-brown
Thanks to @slibkind's PR #433, we now have a first implementation of the left pushforward data migration functor for C-sets. Given a functor F: C -> D between schemas, the algorithm assumes that the graph generating D has no cycles (it performs a topological sort on D). This means that we cannot, for example, create the free reflexive graph on a graph because the schema for reflexive graphs has cycles.
In general, computing left Kan extensions is a challenging problem. The state of the art seems to be Fast Left Kan Extensions using the Chase by Spivak and Wisnesky. For a next step, I think we should just do the simplest thing that would cover standard examples like symmetric and/or reflexive graphs.