Fukaya category

In symplectic topology, a discipline within mathematics, a Fukaya category of a symplectic manifold is a category whose objects are Lagrangian submanifolds of , and morphisms are Floer chain groups: . Its finer structure can be described in the language of quasi categories as an A_∞-category.

They are named after Kenji Fukaya who introduced the language first in the context of Morse homology, and exist in a number of variants. As Fukaya categories are A_∞-categories, they have associated derived categories, which are the subject of a celebrated conjecture of Maxim Kontsevich: the homological mirror symmetry. This conjecture has been verified by computations for a variety of comparatively simple examples.

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