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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 ondoi:10.4310/hha.2007.v9.n2.a6 fatcat:22l3fy7ayrgxdkyqc273ildofy