is_monic for free simple model morphisms, initializing hom search, monic search constraint #204
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kris-brown
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This adds some related features which combine in a test which states (informally)
simple_paths(G, x, y)is equal tohomomorphisms(walking_edge, G; initial=(walking_src -> x, walking_tgt -> y))(in the case of all the object/morphism types being the same). This is done for an arbitrary model with lots of loops, but in general could be a nice thing to property-based-test in the future.Now, a path is simple if it has no repeated generating morphisms (before it couldn't repeat objects except for beginning and end). A model morphism is simple if all generators are sent to simple paths.
This PR additionally adds a check for whether a morphism is monic (conditional on it being free and simple).
Initializing hom search merely adds some clauses to the
searchfunction which check, before looping through possible ob/mor assignments, if the ob/mor has already been preassigned. Future work will go into making this more efficient by playing with the order which the algorithm attempts assignments to improve performance.