General Comodule-Contramodule Correspondence
Abstract
This paper is a fundamental study of comodules and contramodules over a comonoid in a symmetric closed monoidal category. We study both algebraic and homotopical aspects of them. Algebraically, we enrich the comodule and contramodule categories over the original category, construct enriched functors between them and enriched adjunctions between the functors. Homotopically, for simplicial sets and topological spaces, we investigate the categories of comodules and contramodules and the relations between them.
Cite
@article{arxiv.2004.12953,
title = {General Comodule-Contramodule Correspondence},
author = {Katerina Hristova and John Jones and Dmitriy Rumynin},
journal= {arXiv preprint arXiv:2004.12953},
year = {2023}
}
Comments
Version 2: major revision to make the paper easier to read. Version 3: another major revision: we refer to various old results on the functorial semantics that makes paper shorter and more accessible. Version 4: yet another major revision: we replace a biclosed monoidal category with a symmetric closed monoidal category, simplifying many proofs. Version 5: minor edits, final journal version