Interleaved equivalence of categories of persistence modules

TL;DR

This paper establishes a categorical equivalence between two models of persistence modules, one as graded modules over a polynomial ring and the other over the total order of real numbers, using epsilon-interleavings.

Contribution

It introduces an equivalence of categories connecting different algebraic models of persistence modules via epsilon-interleavings.

Findings

Categorical equivalence between two models of persistence modules.

Use of epsilon-interleavings as a fundamental component.

Bridging algebraic and order-theoretic perspectives on persistence modules.

Abstract

We demonstrate that an equivalence of categories using $\varepsilon$-interleavings as a fundamental component exists between the model of persistence modules as graded modules over a polynomial ring and the model of persistence modules as modules over the total order of the real numbers.