Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
extriangulated category; covariantly finite subcategory
extriangulated category; covariantly finite subcategory
Summary:
Extriangulated categories were introduced by Nakaoka and Palu by extracting the similarities between exact categories and triangulated categories. A notion of homotopy cartesian square in an extriangulated category is defined in this article. We prove that in an extriangulated category with enough projective objects, the extension subcategory of two covariantly finite subcategories is covariantly finite. As an application, we give a simultaneous generalization of a result of X. W. Chen (2009) and of a result of R. Gentle, G. Todorov (1996).
References:
[1] Auslander, M., Reiten, I.: Applications of contravariantly finite subcategories. Adv. Math. 86 (1991), 111-152. DOI 10.1016/0001-8708(91)90037-8 | MR 1097029 | Zbl 0774.16006
[2] Barot, M., Kussin, D., Lenzing, H.: The Grothendieck group of a cluster category. J. Pure Appl. Algebra 212 (2008), 33-46. DOI 10.1016/j.jpaa.2007.04.007 | MR 2355032 | Zbl 1148.16005
[3] Beligiannis, A., Reiten, I.: Homological and homotopical aspects of torsion theories. Mem. Amer. Math. Soc. 188 (2007). DOI 10.1090/memo/0883 | MR 2327478 | Zbl 1124.18005
[4] Bühler, T.: Exact categories. Expo. Math. 28 (2010), 1-69. DOI 10.1016/j.exmath.2009.04.004 | MR 2606234 | Zbl 1192.18007
[5] Chen, X. W.: Extensions of covariantly finite subcategories. Arch. Math. 93 (2009), 29-35. DOI 10.1007/s00013-009-0013-8 | MR 2520641 | Zbl 1181.18007
[6] Gentle, R., Todorov, G.: Extensions, kernels and cokernels of homologically finite subcategories. Representation theory of algebras. Seventh international conference, August 22-26, 1994, Cocoyoc, Mexico Bautista, Raymundo et al. American Mathematical Society. CMS Conf. Proc. 18 (1996), 227-235. MR 1388053 | Zbl 0858.18007
[7] Hügel, L. A., Marks, F., Vitória, J.: Silting modules and ring epimorphisms. Adv. Math. 303 (2016), 1044-1076. DOI 10.1016/j.aim.2016.08.035 | MR 3552543 | Zbl 06636662
[8] Iyama, O., Lerner, B.: Tilting bundles on orders on $\mathbb{P}^d$. Isr. J. Math. 211 (2016), 147-169. DOI 10.1007/s11856-015-1263-8 | MR 3474959 | Zbl 1365.14004
[9] Keller, B.: On triangulated orbit categories. Doc. Math. 10 (2005), 21-56. MR 2184464 | Zbl 1086.18006
[10] Mendoza, O., Santiago, V.: Homological systems in triangulated categories. Appl. Categ. Struct. 24 (2016), 1-35. DOI 10.1007/s10485-014-9384-5 | MR 3448426 | Zbl 1336.18004
[11] Nakaoka, H., Palu, Y.: Mutation via Hovey twin cotorsion pairs and model structures in extriangulated categories. Available at https://arxiv.org/abs/1605.05607v2
[12] Zhou, P. Y., Zhu, B.: Triangulated quotient categories revisited. J. Algebra 502 (2018), 196-232. DOI 10.1016/j.jalgebra.2018.01.031 | MR 3774890 | Zbl 06851776
Search
Partner of
