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# 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

#### Author

#### Abstract

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.

#### Keywords

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

#### 2010 Mathematics Subject Classification

18D05, 18D20, 18G55, 57Txx

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