Strong shift equivalence as a category notion

TL;DR

This paper connects the conjugacy problem in symbolic dynamics to category theory, specifically traced bialgebras, providing a new categorical perspective and invariants for the problem.

Contribution

It introduces a novel categorical approach to the conjugacy problem using traced bialgebras, offering new invariants and insights.

Findings

Establishes a link between symbolic dynamics and category theory.

Provides a systematic method for deriving invariants from bialgebras.

Suggests a new perspective on the conjugacy problem through category theory.

Abstract

In this paper, we present a completely radical way to investigate the main problem of symbolic dynamics, the conjugacy problem, by proving that this problem actually relates to a natural question in category theory regarding the theory of traced bialgebras. As a consequence of this theory, we obtain a systematic way of obtaining new invariants for the conjugacy problem by looking at existing bialgebras in the literature.