Geodesic
Homotopy Properties of $\infty$-Simplicial Coalgebras and Homotopy Unital Supplemented $A_\infty$-Algebras
Matematičeskie zametki, Tome 99 (2016) no. 1, pp. 55-77.

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The homotopy theory of $\infty$-simplicial coalgebras is developed; in terms of this theory, an additional structure on the tensor bigraded coalgebra of a graded module is described such that endowing the coalgebra with this structure is equivalent to endowing the given graded module with the structure of a homotopy unital $A_\infty$-algebra.
Keywords: homotopy theory of $\infty$-simplicial coalgebras, differential $\infty$-simplicial module, homotopy unital augmented $A_\infty$-algebra, tensor bigraded coalgebra of a graded module, connected graded module, SDR-data. 
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S. V. Lapin. Homotopy Properties of $\infty$-Simplicial Coalgebras and Homotopy Unital Supplemented $A_\infty$-Algebras. Matematičeskie zametki, Tome 99 (2016) no. 1, pp. 55-77. http://geodesic.mathdoc.fr/item/MZM_2016_99_1_a5/

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