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Hovey pairs in $\mathbb{C}_N(\mathcal{G})$ | ||
| Journal of Algebra and Related Topics | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 06 دی 1404 | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2025.30423.1791 | ||
| نویسندگان | ||
| J. Nazaripour؛ P. Bahiraei* | ||
| Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran | ||
| چکیده | ||
| 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 $\mathbb{X}$. | ||
| کلیدواژهها | ||
| $N$-complexes؛ Complete cotorsion pairs؛ Model structure؛ Hovey pair | ||
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آمار تعداد مشاهده مقاله: 5 |
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