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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJan 5th 2019
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded publication data for * [[Maxim Kontsevich]], [[Yan Soibelman]], _Notes on $A_\infty$-algebras, $A_\infty$-categories and non-commutative geometry. I_, in [[Anton Kapustin]], [[Maximilian Kreuzer]], [[Karl-Georg Schlesinger]] (eds.) _Homological mirror symmetry -- New developments and perspectives_, Springer 2008 ([arXiv:math/0606241](http://arxiv.org/abs/math/0606241), [doi:10.1007/978-3-540-68030-7](https://www.springer.com/de/book/9783540680291)) <a href="https://ncatlab.org/nlab/revision/diff/A-infinity-category/33">diff</a>, <a href="https://ncatlab.org/nlab/revision/A-infinity-category/33">v33</a>, <a href="https://ncatlab.org/nlab/show/A-infinity-category">current</a>

   added publication data for

   • Maxim Kontsevich, Yan Soibelman, Notes on $A_\infty$-algebras, $A_\infty$-categories and non-commutative geometry. I, in Anton Kapustin, Maximilian Kreuzer, Karl-Georg Schlesinger (eds.) Homological mirror symmetry – New developments and perspectives, Springer 2008 (arXiv:math/0606241, doi:10.1007/978-3-540-68030-7)

   diff, v33, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMar 13th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to today's * Yong-Geun Oh, [[Hiro Lee Tanaka]], _$A_\infty$-categories, their $\infty$-categories, and their localizations_ ([arXiv:2003.05806](https://arxiv.org/abs/2003.05806)) <a href="https://ncatlab.org/nlab/revision/diff/A-infinity-category/35">diff</a>, <a href="https://ncatlab.org/nlab/revision/A-infinity-category/35">v35</a>, <a href="https://ncatlab.org/nlab/show/A-infinity-category">current</a>

   added pointer to today’s

   • Yong-Geun Oh, Hiro Lee Tanaka, $A_\infty$-categories, their $\infty$-categories, and their localizations (arXiv:2003.05806)

   diff, v35, current

3. • CommentRowNumber3.
   • CommentAuthorGuest
   • CommentTimeOct 8th 2022
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   Author: Guest
   Format: Text"If the composition in the linear A_\infty-category does happen to be strictly associative it becomes the same as a dg-category." Are you sure about this? For A_\infty algebras it's false. A good example is the cohomology of a space. This is strictly associative but inherits an A_\infty structure from the cochains via Kadeishvili's theorem, and it's usually not formal. Comment by Dave Benson, University of Aberdeen.

   "If the composition in the linear A_\infty-category does happen to be strictly associative it becomes the same as a dg-category."
   Are you sure about this? For A_\infty algebras it's false. A good example is the cohomology of a space. This is strictly associative
   but inherits an A_\infty structure from the cochains via Kadeishvili's theorem, and it's usually not formal.
   Comment by Dave Benson, University of Aberdeen.
4. • CommentRowNumber4.
   • CommentAuthorDmitri Pavlov
   • CommentTimeOct 8th 2022
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexCorrection: If higher coherences in a linear $A_\infty$-category happen to be equal to identity morphisms (which is encoded by the vanishing of the maps $m_n$ for $n\ge3$, defined below), it becomes the same as a [[dg-category]]. <a href="https://ncatlab.org/nlab/revision/diff/A-infinity-category/36">diff</a>, <a href="https://ncatlab.org/nlab/revision/A-infinity-category/36">v36</a>, <a href="https://ncatlab.org/nlab/show/A-infinity-category">current</a>

   Correction:

   If higher coherences in a linear $A_\infty$-category happen to be equal to identity morphisms (which is encoded by the vanishing of the maps $m_n$ for $n\ge3$, defined below), it becomes the same as a dg-category.

   diff, v36, current

5. • CommentRowNumber5.
   • CommentAuthorzskoda
   • CommentTimeOct 18th 2022
   • PermaLink
   Author: zskoda
   Format: MarkdownItexThe pdf of Homotopy theory of homotopy algebras at the ex-page of [[Bruno Valette]] does not work as he changed the university since and there is a new page but with some book links not working. But the paper is available at regular sources so it is updated now * [[Bruno Valette]], _Homotopy theory of homotopy algebras_, Annales de l'Institut Fourier __70__:2 (2020) 683--738 [doi](https://10.5802/aif.3322) [Zbl:1335.18001](https://zbmath.org/?q=an:1335.18001) [arXiv:1411.5533](https://arxiv.org/abs/1411.5533) <a href="https://ncatlab.org/nlab/revision/diff/A-infinity-category/37">diff</a>, <a href="https://ncatlab.org/nlab/revision/A-infinity-category/37">v37</a>, <a href="https://ncatlab.org/nlab/show/A-infinity-category">current</a>

   The pdf of Homotopy theory of homotopy algebras at the ex-page of Bruno Valette does not work as he changed the university since and there is a new page but with some book links not working. But the paper is available at regular sources so it is updated now

   • Bruno Valette, Homotopy theory of homotopy algebras, Annales de l’Institut Fourier 70:2 (2020) 683–738 doi Zbl:1335.18001 arXiv:1411.5533

   diff, v37, current