Homotopy Transfer Theorem

A result asserting that algebraic structures defined on a chain-level model (for example a differential graded algebra or Lie algebra) can be transferred along a homotopy equivalence or contraction to a quasi-isomorphic model (often the cohomology) as a homotopy algebra (e.g., A_∞- or L_∞-structure), with explicitly defined higher operations encoding the obstruction data.