Category of A_infinity-categories

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We define natural A_infinity-transformations and construct A_infinity-category of A_infinity-functors. The notion of non-strict units in an A_infinity-category is introduced. The 2-category of (unital) A_infinity-categories, (unital) functors and transformations is described.
51 pages, LaTeX, uses Paul Taylor's diagrams.sty. It is the published text plus my comments in blue in the places that are hard to read: omissions, difficult proofs, ambiguities. An error is corrected in red

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