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The dihedral homology functor $HD:A_\infty^{{\rm inv}}(K)\to GrM(K)$ from thecategory $A_\infty^{{\rm inv}}(K)$ of involutive $A_\infty$-algebras over anycommutative unital ring $K$ to the category $GrM(K)$ of graded $K$-modules isconstructed. Further, it is showed that this functor sends homotopyequivalences of involutive $A_\infty$-algebras into isomorphisms of gradedmodules.

The homotopy invariance of dihedral homology of involutive $A_\infty$-algebras over rings