Full and convex linear subcategories are incompressible

TL;DR

This paper proves that full convex subcategories of linear categories have injective fundamental group maps, establishing their incompressibility through functoriality of the intrinsic fundamental group and connected gradings.

Contribution

It introduces the concept that full convex subcategories are incompressible by demonstrating the injectivity of the fundamental group map, based on functoriality and gradings.

Findings

Full convex subcategories are incompressible.

Fundamental group maps are injective for these subcategories.

Functoriality of the fundamental group is established.

Abstract

Consider the intrinsic fundamental group \`a la Grothendieck of a linear category using connected gradings. In this article we prove that any full convex subcategory is incompressible, in the sense that the group map between the corresponding fundamental groups is injective. We start by proving the functoriality of the intrinsic fundamental group with respect to full subcategories, based on the study of the restriction of connected gradings.