The fundamental group functor as a Kan extension

TL;DR

This paper demonstrates that the fundamental group functor in categorical Galois theory can be calculated using the mathematical concept of Kan extension, providing a new perspective on its computation.

Contribution

It establishes that the fundamental group functor is a Kan extension, linking categorical Galois theory with a key concept in category theory.

Findings

Fundamental group functor can be computed as a Kan extension.

Provides a new categorical perspective on fundamental groups.

Bridges categorical Galois theory with Kan extension theory.

Abstract

We prove that the fundamental group functor from categorical Galois theory may be computed as a Kan extension.