Phillip Hackney: Modules and excision

If a manifold M decomposes as R ∪ L, glued along a submanifold N×ℝ, then F_R(A) and F_L(A) are modules over the E^1 algebra F_{N×ℝ}(A). The excision axiom for factorization homology says that the map from the derived tensor product F_R(A) ⊗ F_L(A) to F_M(A) is an equivalence. We will attempt to make precise what this statement says; in particular, we talk about algebras over ∞-operads, modules over such, and why the chain complexes from the first sentence give examples.