On Conjugates and Adjoint Descent

TL;DR

This paper introduces an $ abla$-categorical framework for descent along adjunctions and provides a universal formula for counting conjugates up to equivalence, unifying various known results across fields.

Contribution

It develops a general $ abla$-categorical approach to descent and conjugate counting, unifying multiple existing formulas in a broad theoretical framework.

Findings

Unified formula for counting conjugates up to equivalence.

Framework applies to various fields through $ abla$-categorical methods.

Provides a general approach to descent along adjunctions.

Abstract

In this note we present an $\infty$-categorical framework for descent along adjunctions and a general formula for counting conjugates up to equivalence which unifies several known formulae from different fields.