On the Categorification of the M\"obius Function

TL;DR

This paper explores categorical generalizations of the M"obius function, highlighting their topological and geometric interpretations, and discusses how different approaches relate to each other.

Contribution

It introduces new categorical frameworks for the M"obius function and clarifies their connections and geometric significance.

Findings

Categorical generalizations of the M"obius function are developed.

Connections between different categorical approaches are established.

Topological and geometric interpretations are emphasized.

Abstract

In these notes we study several categorical generalizations of the M\"obius function and discuss the relations between the various approaches. We emphasize the topological and geometric meaning of these constructions.