@article{Mbarga_2022, title={Homomorphic Relations and Goursat Lemma}, volume={10}, url={https://earthlinepublishers.com/index.php/ejms/article/view/537}, DOI={10.34198/ejms.10122.169181}, abstractNote={<p>Over the past years various authors have investigated the famous elementary result in group theory called Goursat’s lemma for characterizing the subgroups of the direct product $A\times B$ of two groups $A,B$. Given a homomorphic relation $\rho = (R,A,B)$ where $A$ and $B$ are groups and $R$ is a subgroup of $A\times B.$ What can one say about the structure of $\rho$. In 1950 Riguet proved a theorem that allows us to obtain a characterization of $\rho$ induces by examining the sections of the direct factors. The purpose of this paper is two-fold. A first and more concrete aim is to provide a containment relation property between homomorphic relation. Indeed if $\rho,\sigma$ are homomorphic relations, we provide necessary and sufficient conditions for $\sigma\leq\rho$. A second and more abstract aim is to introduce a generalization of some notions in homological algebra. We define the concepts of $\theta$-exact. We also obtain some interesting results. We use these results to find a generalization of Lambek Lemma.</p>}, number={1}, journal={Earthline Journal of Mathematical Sciences}, author={Mbarga, Brice Réné Amougou}, year={2022}, month={Jun.}, pages={169-181} }