Monomial ideals admit pivot resolutions that sit between Lyubeznik and Taylor resolutions, always carry a DG-algebra structure, and come with explicit Eisenbud-Shamash higher homotopies over complete intersections.
Avramov, Obstructions to the existence of multiplicative structure s on minimal free resolutions , American Journal of Mathematics 103 (1981), 1
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A family of simplicial resolutions which are DG-algebras
Monomial ideals admit pivot resolutions that sit between Lyubeznik and Taylor resolutions, always carry a DG-algebra structure, and come with explicit Eisenbud-Shamash higher homotopies over complete intersections.