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Sigma migration of morphisms #937

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Sigma migration of morphisms #937

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kris-brown
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@kris-brown kris-brown commented Sep 11, 2024

This PR allows one to call sigma migration objects as if they were functions on both ACSets and ACSetTransformations.

Sigma migration along F: C -> D on morphisms begins with migrating the dom, X, and codom, Y.

The new components, e.g. for some object a in the schema C which is sent to an object, are the unique ones
which make the following square commute:

                         fₐ
               Xₐ      →     Yₐ        
         αXₐ ↓              ↓ αYₐ
      ΣF(X)_F(a) ⤑ ΣF(Y)_F(a)

This is because the results of the sigma migrations are freely generated by some
generators, and we stipulate the homomorphism by saying where the generators go via an initialized hom search.

There are some deeper issues that need to be addressed, unrelated to SigmaMigrations but rather to VarACSets, which are uncovered by migrations in AlgRewriting now stress-testing the chase with AttrVars. I'll update this description with details on this later!

working draft for SimpleMigrations
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