### A closer look at Kadeishvili's theorem

#### Abstract

We give a proof of the Homotopy Transfer Theorem following Kadeishvili's original strategy. Although Kadeishvili originally restricted himself to transferring a dg algebra structure to an A-infinity-structure on homology, we will see that a small modification of his argument proves the general case of transferring any kind of infinity-algebra structure along a quasi-isomorphism, under weaker hypotheses than existing proofs of this result.

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