Entropy in a category

TL;DR

This paper generalizes the concept of Pinsker subgroups to an abelian category setting by introducing an entropy function and defining a Pinsker radical, linking it to torsion theories.

Contribution

It extends the Pinsker subgroup concept from abelian groups to abelian categories via a new entropy function and Pinsker radical, establishing a torsion theory framework.

Findings

Defined an entropy function h for abelian categories

Introduced the Pinsker radical with respect to h

Connected the Pinsker radical to torsion classes

Abstract

The Pinsker subgroup of an abelian group with respect to an endomorphism was introduced in the context of algebraic entropy. Motivated by the nice properties and characterizations of the Pinsker subgroup, we generalize its construction in two directions. We introduce the concept of entropy function h of an abelian category and define the Pinsker radical with respect to h, so that the class of all objects with trivial Pinsker radical is the torsion class of a torsion theory.