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A symplectic Lie groupoid is a Lie groupoid with aÌý
multiplicative symplectic form. We take the perspective that such anÌý
object is symplectic manifold with an extra categorical structure.Ìý
Applying the machinery of Floer theory, the extra structure is expectedÌý
to yield a monoidal structure on the Fukaya category, and new operationsÌý
on the closed string invariants. I will take an examples-based approachÌý
to working out what these structures are, focusing on cases where theÌý
Floer theory is tractable, such as the cotangent bundle of a compactÌý
manifold.