# Homological Algebra of Heyting modules

## TL;DR

This paper develops a non-abelian homological theory for modules over Heyting algebras, connecting topology, logic, and algebra to extend the understanding of these structures.

## Contribution

It introduces a novel homological framework for modules over Heyting algebras, bridging non-abelian algebraic methods with logical and topological structures.

## Key findings

- Established a homological theory for Heyting modules
- Connected Heyting algebra properties with module theory
- Provided foundational results for future research

## Abstract

The collection of open sets of a topological space forms a Heyting algebra, which leads to the idea of a Heyting algebra as a generalized topological space. In fact, a sober topological space may be reconstructed from its locale of open sets. This has given rise to a good theory of presheaves and sheaves over locales. At the same time, several ring like properties of Heyting algebras have also been studied. The purpose of this paper is to study a non-abelian homological theory for modules over Heyting algebras.