On representation categories of $A_\infty$-algebras and $A_\infty$-coalgebras

Abhishek Banerjee; Anita Naolekar

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arXiv · 2112.02707

On representation categories of $A_\infty$-algebras and $A_\infty$-coalgebras

Abhishek Banerjee·Anita Naolekar

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Abstract

In this paper, we use the language of monads, comonads and Eilenberg-Moore categories to describe a categorical framework for $A_\infty$-algebras and $A_\infty$-coalgebras, as well as $A_\infty$-modules and $A_\infty$-comodules over them respectively. The resulting formalism leads us to investigate relations between representation categories of $A_\infty$-algebras and $A_\infty$-coalgebras. In particular, we relate $A_\infty$-comodules and $A_\infty$-modules by considering a rational pairing between an $A_\infty$-coalgebra $C$ and an $A_\infty$-algebra $A$. The categorical framework also motivates us to introduce $A_\infty$-contramodules over an $A_\infty$-coalgebra $C$.

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BibTeX RIS

Abhishek Banerjee, Anita Naolekar. 2021-12-05. On representation categories of $A_\infty$-algebras and $A_\infty$-coalgebras. https://arxiv.org/abs/2112.02707

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