Incremental homomorphism search

[kris-brown]

In many applications, we have a sequence of C-Sets (X1->X2->X3->...) over time, connected by morphisms. We wish to find all matches of some pattern at every step. The C-Sets may differ only in a small region, so an algorithm like this is needed to avoid recomputing the entire set of matches (something that scales with the size of the change, not the size of the entire C-Set Xn).

A fairly recent summary of this is found here

This would immediately find applications in at least three areas:

• pushout based chase
• AlgebraicRewriting simulations
• finite limit sketch models (finding which limit cones changed after a small update)

[kris-brown]

Another reference: https://www.irif.fr/~jkrivine/download/esop_revised.pdf