Homology, Homotopy and Applications

Volume 5 (2003)

Number 1

Category of $A_{\infty}$-categories

Pages: 1 – 48

DOI: http://dx.doi.org/10.4310/HHA.2003.v5.n1.a1


Volodymyr Lyubashenko (Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine)


We define natural $A_{\infty}$-transformations and construct $A_{\infty}$-category of $A_{\infty}$-functors. The notion of non-strict units in an $A_{\infty}$-category is introduced. The 2-category of (unital) $A_{\infty}$-categories, (unital) functors and transformations is described.


$A_{\infty}$-categories, $A_{\infty}$-functors, $A_{\infty}$-transformations, unit $A_{\infty}$-transformation, 2-category

2010 Mathematics Subject Classification

18D05, 18D20, 18G55, 57Txx

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An erratum to this article is available as HHA 9(2) pp. 163-164.