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For questions about Fukaya categories (as introduced by Fukaya in 1993) and their structure; consider also related tags such as [floer-homology] or [lagrangian-submanifolds].

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Is there any work on "super Fukaya categories"?

There is a well-established notion of "supermanifold", and in the world of supergeometry it makes sense to talk about symplectic structures. Actually, there are various kinds of symplectic structures …
Theo Johnson-Freyd's user avatar