Erratum to "Category of $A_{\infty}$-categories"

Volodymyr Lyubashenko
2007 Homology, Homotopy and Applications  
The erroneous statement (HHA 5 (2003), no. 1, 1-48) that the collection of unital A ∞ -categories, all A ∞ -functors, and all A ∞ -transformations (resp. equivalence classes of natural A ∞transformations) form a K-2-category K u A ∞ (resp. ordinary 2-category u A ∞ ) is corrected as follows. All 2-category axioms are satisfied, except that 1 e · f does not necessarily equal 1 ef for all composable 1-morphisms e, f . The axiom e · 1 f = 1 ef does hold. The mistake does not affect results on
more » ... tible 2-morphisms and quasi-invertible 1-morphisms in u A ∞ .
doi:10.4310/hha.2007.v9.n2.a6 fatcat:22l3fy7ayrgxdkyqc273ildofy