# 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 the celebrated homological mirror symmetry conjecture of Maxim Kontsevich. This conjecture has been computationally verified for a number of comparatively simple examples.

## References

- P. Seidel,
*Fukaya categories and Picard-Lefschetz theory*, Zurich lectures in Advanced Mathematics - Fukaya, Y-G. Oh, H. Ohta, K. Ono,
*Lagrangian Intersection Floer Theory*, Studies in Advanced Mathematics - The thread on MathOverflow 'Is the Fukaya category "defined"?'

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