## Homology, Homotopy and Applications

### Erratum to Category of $A_\infty$-categories'

Volodymyr Lyubashenko

#### Abstract

The erroneous statement (HHA 5 (2003), no. 1, 1–48) that the collection of unital $A_\infty$-categories, all $A_\infty$-functors, and all $A_\infty$-transformations (resp. equivalence classes of natural $A_\infty$- transformations) form a $\mathcal{K}-2$-category $\mathcal{K}^u A_\infty$(resp. ordinary 2-category $^u A_\infty$) is corrected as follows. All 2-category axioms are satisfied, except that $1_e \cdot f$ does not necessarily equal $1_{ef}$ for all composable 1-morphisms $e, f$. The axiom $e \cdot 1_f = 1_{ef}$ does hold. The mistake does not affect results on invertible 2-morphisms and quasi-invertible 1-morphisms in $^u A_\infty$.

#### Article information

Source
Homology Homotopy Appl., Volume 9, Number 2 (2007), 163-164.

Dates
First available in Project Euclid: 23 January 2008

Permanent link to this document
https://projecteuclid.org/euclid.hha/1201127335

Mathematical Reviews number (MathSciNet)
MR2366947

Zentralblatt MATH identifier
1120.18004

#### Citation

Lyubashenko, Volodymyr. Erratum to Category of $A_\infty$-categories'. Homology Homotopy Appl. 9 (2007), no. 2, 163--164. https://projecteuclid.org/euclid.hha/1201127335

• See original article: Volodymyr Lyubashenko. Category of $A\sb \infty$-categories. Homology Homotopy Appl. Volume 5, Number 1 (2003), 1-48.