2021/12/05 by Abhishek Banerjee, Banerjee, Abhishek, Anita Naolekar +1
Mathematics · #18C15 #18C20 #18G70 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2112.02707
openalex publication_date 2021/12/05 · openalex created_date 2021/12/31 · openalex updated_date 2026/07/28
In this paper, we use the language of monads, comonads and Eilenberg-Moore categories to describe a categorical framework for A_∞-algebras and A_∞-coalgebras, as well as A_∞-modules and A_∞-comodules over them respectively. The resulting formalism leads us to investigate relations between representation categories of A_∞-algebras and A_∞-coalgebras. In particular, we relate A_∞-comodules and A_∞-modules by considering a rational pairing between an A_∞-coalgebra C and an A_∞-algebra A. The categorical framework also motivates us to introduce A_∞-contramodules over an A_∞-coalgebra C.