Galois correspondence for augmented monads

TL;DR

This paper develops a Galois correspondence framework linking sub-monads and sub-functors in augmented monads, providing explicit computation methods and characterizations within monoidal closed categories.

Contribution

It introduces a Galois connection for augmented monads, detailing invariants, stabilizers, and their computation, with applications to Tannakian reconstruction.

Findings

Established a Galois connection between sub-monads and sub-functors.

Provided explicit procedures for computing invariants.

Characterized stabilizers in monoidal closed categories.

Abstract

We establish a Galois connection between sub-monads of an augmented monad and sub-functors of the forgetful functor from its Eilenberg-Moore category. This connection is given in terms of invariants and stabilizers defined through universal properties. An explicit procedure for the computation of invariants is given assuming the existence of suitable right adjoints. Additionally, in the context of monoidal closed categories, a characterization of stabilizers is made in terms of Tannakian reconstruction.