# Cup-product in Hom-Leibniz cohomology and Hom-Zinbiel algebras

## TL;DR

This paper introduces a cup-product in Hom-Leibniz cohomology and demonstrates that it satisfies the graded Hom-Zinbiel relation, expanding the algebraic structures in Hom-cohomology theories.

## Contribution

It defines a new cup-product in Hom-Leibniz cohomology and proves its relation to Hom-Zinbiel algebra structures, which is a novel theoretical development.

## Key findings

- Cup-product in Hom-Leibniz cohomology is defined.
- The cup-product satisfies the graded Hom-Zinbiel relation.
- Establishes a new connection between Hom-Leibniz and Hom-Zinbiel algebraic structures.

## Abstract

We define a cup-product in Hom-Leibniz cohomology and show that the cup-product satisfies the graded Hom-Zinbiel relation.