The tensor functor from the category of A_∞-algebras into the category of differential modules with ∞-simplicial faces

2019/03/03 by С. В. Лапин, S. V. Lapin, Lapin, S. V.
Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.AT #math.KT

paper · pdf · doi:10.48550/arxiv.1903.00869

arxiv created 2019/03/03 · openalex publication_date 2019/03/03 · arxiv updated 2019/03/05 · openalex created_date 2019/03/11 · openalex updated_date 2026/07/28

Abstract

The tensor functor from the category of A_∞-algebras into the category of differential modules with ∞-simplicial faces is constructed. Further, it is showed that this functor sends homotopy equivalent A_∞-algebras into homotopy equivalent differential modules with ∞-simplicial faces.

Related

• Differential modules with ∞-simplicial faces and A_∞-algebras
• Tensor product of A_∞-categories
• An Alternative to Homotopy Transfer for A_∞-Algebras
• Homotopical properties of the simplicial Maurer-Cartan functor
• Dihedral and reflexive modules with ∞-simplicial faces and dihedral and reflexive homology of involutive A_∞-algebras over unital commutative rings