A remark to "A note on the Fundamental Group of a Triangular Algebra", by F.Xu

TL;DR

This paper presents a counter-example challenging a previously claimed proposition about the fundamental group of a triangular algebra, highlighting the need for revision in the existing theoretical framework.

Contribution

It introduces a specific counter-example that refutes Proposition 3.2 in F. Xu's work, advancing the understanding of algebraic fundamental groups.

Findings

Counter-example disproves Proposition 3.2

Refines understanding of fundamental groups in triangular algebras

Highlights gaps in previous theoretical assumptions

Abstract

We provide a counter-example to Proposition 3.2 of "A note on the Fundamental Group of a Triangular Algebra", by F.Xu.