# Digital Hurewicz Theorem and Digital Homology Theory

## TL;DR

This paper develops a homology theory for digital images based on cubical singular homology, establishing a digital Hurewicz theorem and properties similar to classical homology axioms.

## Contribution

It introduces a novel digital homology framework that parallels classical homology theories, including a digital Hurewicz theorem and axioms for digital homology.

## Key findings

- Established digital homology groups for digital images.
- Proved a digital Hurewicz theorem relating fundamental group and homology.
- Showed homology functors satisfy properties similar to Eilenberg-Steenrod axioms.

## Abstract

In this paper, we develop homology groups for digital images based on cubical singular homology theory for topological spaces. Using this homology, we present digital Hurewicz theorem for the fundamental group of digital images. We also show that the homology functors developed in this paper satisfy properties that resemble the Eilenberg-Steenrod axioms of homology theory, in particular, the homotopy and the excision axioms. We finally define axioms of digital homology theory.