Construction of an analogue of simplicial degenerations in the $A_\infty$-case

The article considers the construction of $A_\infty$-case simplicial degeneracy analogue. The author presents a design of higher facets, proves their existence on the homology, and addresses the effect of the differential on this site. As the proof of the existence theorem is constructive, it allows to construct new objects on the homology of chain complexes. While proving the theorems the author used the technique of SDR-situations.