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 $\mathcal{A}$ 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 $\mathbb{X}$.
Nazaripour, J. and Bahiraei, P. (2025). Hovey pairs in $\mathbb{C}_N(\mathcal{G})$. Journal of Algebra and Related Topics, (), -. doi: 10.22124/jart.2025.30423.1791
MLA
Nazaripour, J. , and Bahiraei, P. . "Hovey pairs in $\mathbb{C}_N(\mathcal{G})$", Journal of Algebra and Related Topics, , , 2025, -. doi: 10.22124/jart.2025.30423.1791
HARVARD
Nazaripour, J., Bahiraei, P. (2025). 'Hovey pairs in $\mathbb{C}_N(\mathcal{G})$', Journal of Algebra and Related Topics, (), pp. -. doi: 10.22124/jart.2025.30423.1791
CHICAGO
J. Nazaripour and P. Bahiraei, "Hovey pairs in $\mathbb{C}_N(\mathcal{G})$," Journal of Algebra and Related Topics, (2025): -, doi: 10.22124/jart.2025.30423.1791
VANCOUVER
Nazaripour, J., Bahiraei, P. Hovey pairs in $\mathbb{C}_N(\mathcal{G})$. Journal of Algebra and Related Topics, 2025; (): -. doi: 10.22124/jart.2025.30423.1791
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