Classification of twisted free tensor products (Q911100)

Let A be a differential graded algebra, B a differential graded coalgebra and let TB denote the tensor algebra over B. The author defines the twisted free tensor product \(TB\coprod_ xA\) with twisting cochain x: \(B\to A\) and proves the following Theorem: There is a 1-1 correspondence between the set of equivalence classes of twisted free tensor products with fixed cobase TB and cofibre A and the set of homotopy classes of coalgebra maps from B to the bar construction \({\mathcal B}(A)\).