Homology, Homotopy and Applications

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

Volodymyr Lyubashenko

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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

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

First available in Project Euclid: 23 January 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 18D05: Double categories, 2-categories, bicategories and generalizations 18D20: Enriched categories (over closed or monoidal categories) 18G55: Homotopical algebra 57T30: Bar and cobar constructions [See also 18G55, 55Uxx]


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

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See also

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