# Comparison between "Parametrized homology via zigzag persistence" and "Refined homology in the presence of a real-valued continuous function"

## TL;DR

This paper demonstrates that certain persistence diagrams and measures from previous works are special cases of more general maps and measures, unifying different approaches in parametrized and refined homology.

## Contribution

It shows that the persistence diagrams and measures in [5] are specific instances of the more general frameworks discussed in [2] and [1], unifying different homology approaches.

## Key findings

- Persistence diagrams in [5] are special cases of maps in [2] and [1]
- Measures in [5] are particular cases of those in [2] and [1]
- Unification of parametrized and refined homology frameworks

## Abstract

In this note one shows that the four persistence diagrams and measures defined in [5] are particular cases of the maps and the measures discussed in [2] and [1]