A general method for building reflections

TL;DR

This paper introduces a universal method for constructing reflections between categories, enabling the derivation of known and new adjunctions, including those related to geometric morphisms and Stone-type dualities.

Contribution

The authors develop a general framework for generating reflections, unifying and extending existing adjunctions in category theory, especially in topos theory.

Findings

Recovered several well-known Stone-type adjunctions

Generated new adjunctions from geometric morphisms

Provided a unified method applicable to various categorical contexts

Abstract

We establish a general method for generating reflections between categories. We then apply our technique to generate adjunctions starting from geometric morphisms between Grothendieck toposes; as particular cases, we recover various well-known Stone-type adjunctions and establish several new ones.