Functoriality for Lagrangian correspondences in Floer theory

Understand

Using quilted Floer cohomology and relative quilt invariants, we define a composition functor for categories of Lagrangian correspondences in monotone and exact symplectic Floer theory.

• We show that this functor agrees with geometric composition in the case that the composition is smooth and embedded.
• As a consequence we obtain 'categorification commutes with composition' for Lagrangian correspondences.