University of Guilan Journal of Algebra and Related Topics 2345-3931 Articles in Press 2025 12 27 Hovey pairs in $\mathbb{C}_N(\mathcal{G})$ 9323 10.22124/jart.2025.30423.1791 EN J. Nazaripour Department of Pure Mathematics‎, ‎Faculty of Mathematical Sciences‎, ‎University of Guilan‎, ‎Rasht‎, ‎Iran P. Bahiraei Department of Pure Mathematics‎, ‎Faculty of Mathematical Sciences‎, ‎University of Guilan‎, ‎Rasht‎, ‎Iran Journal Article 2025 04 19 One approach to construct a model structure on $C_N(\mathcal{A})$, the category of $N$-complexes over an abelian category $\mathcal{A}$, is to start with a complete hereditary cotorsion pair $(\mathcal{F},\mathcal{C})$ in <br />$\mathcal{A}$ and then introduce Hovey pairs on $C_N(\mathcal{A})$. There are three important pairs of cotorsion pairs in the literature. In this paper, we employ a different technique by considering $\mathcal{A}$ as a Grothendieck category to introduce these Hovey pairs. For these pairs of cotorsion pairs, we omit the hereditary conditions, the conditions of having enough $\mathcal{F}$-objects as well as the condition of being closed under direct limits for the class $\mathcal{F}$. So we can construct Hovey pairs on categories that do not necessarily have enough $\mathcal{F}$-objects or where the class of objects is not closed under direct limits such as the category of Cartesian modules over small categories and the category of quasi-coherent sheaves on a scheme $\mathbb{X}$. https://jart.guilan.ac.ir/article_9323_5f145c8405e8c12eb7b56d7627d38b68.pdf