Notes on A∞-Algebras, A∞-Categories and Non-Commutative Geometry

@article{Kontsevich2008NotesOA,
  title={Notes on A∞-Algebras, A∞-Categories and Non-Commutative Geometry},
  author={Maxim Kontsevich and Yan S. Soibelman},
  journal={Lecture Notes in Physics},
  year={2008},
  volume={757},
  pages={153-220}
}
We develop a geometric approach to A-infinity algebras and A-infinity categories based on the notion of formal scheme in the category of graded vector spaces. The geometric approach clarifies several questions, e.g. the notion of homological unit or A-infinity structure on A-infinity functors. We discuss Hochschild complexes of A-infinity algebras from the geometric point of view. The chapter contains homological versions of the notions of properness and smoothness of projective varieties as… 
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