• Corpus ID: 119177357

Notes on A-infinity algebras, A-infinity categories and non-commutative geometry. I

  title={Notes on A-infinity algebras, A-infinity categories and non-commutative geometry. I},
  author={Maxim Kontsevich and Yan S. Soibelman},
  journal={arXiv: Rings and Algebras},
We develop geometric approach to A-infinity algebras and A-infinity categories based on the notion of formal scheme in the category of graded vector spaces. 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 geometric point of view. The paper contains homological versions of the notions of properness and smoothness of projective varieties as well as the… 
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