The Euler characteristic of a bicategory and the product formula for fibered bicategories

TL;DR

This paper explores the Euler characteristic of bicategories, demonstrating its invariance under biequivalence and establishing a product formula for fibered bicategories, extending the concept of magnitude to higher categorical structures.

Contribution

It introduces the Euler characteristic for bicategories, proves its invariance under biequivalence, and derives a product formula for fibered bicategories, advancing categorical invariants.

Findings

Euler characteristic is invariant under biequivalence

Established a product formula for fibered bicategories

Extended magnitude concepts to bicategorical structures

Abstract

This paper studies the Euler characteristic of a bicategory based on the concept of magnitudes introduced by Leinster. We focus on its invariance with respect to biequivalence and on the product formula for Buckley's fibered bicategories.