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Locally finite triangulated categories
Journal of Algebra, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bin Zhu
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gmj, 2006
Abstract The concept of a triangulated homotopy category can be canonically lifted to the level of a groupoid-enriched category. This way two natural axioms on track triangles replace the four somewhat obscure axioms of a triangulated category.
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Abstract The concept of a triangulated homotopy category can be canonically lifted to the level of a groupoid-enriched category. This way two natural axioms on track triangles replace the four somewhat obscure axioms of a triangulated category.
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On Finite Resolutions in Triangulated Categories
Bulletin of the Malaysian Mathematical Sciences Society, 2018\textit{M. Auslander} and \textit{R.-O. Buchweitz} [Mem. Soc. Math. France 38, 5--37 (1989; Zbl 0697.13005)] studied maximal Cohen-Macaulay approximations for certain modules. Recently, \textit{O. Hernández} et al. [Appl. Categ. Struct. 21, No. 2, 119--139 (2013; Zbl 1319.18003)] developed an analogous theory of approximations in the sense of Auslander
Di, Zhenxing, Wang, Pengfei
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2006
AbstractReviewing the basic notions of additive and abelian categories, left and right adjoint functors, and Serre functors, this chapter is mainly devoted to triangulated categories. In particular, criteria are established which decide when a given functor is fully-faithful or an equivalence. This is formulated in terms of spanning classes.
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AbstractReviewing the basic notions of additive and abelian categories, left and right adjoint functors, and Serre functors, this chapter is mainly devoted to triangulated categories. In particular, criteria are established which decide when a given functor is fully-faithful or an equivalence. This is formulated in terms of spanning classes.
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Relative Quotient Triangulated Categories
Algebra Colloquium, 2014Let A be a finite dimensional algebra over a field k. We consider a subfunctor F of [Formula: see text], which has enough projectives and injectives such that [Formula: see text] is of finite type, where [Formula: see text] denotes the set of F-projectives. One can get the relative derived category [Formula: see text] of A-mod.
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Triangulated equivalence between a homotopy category and a triangulated quotient category
Journal of Algebra, 2018\textit{M. Hovey} [Math. Z. 241, No. 3, 553--592 (2002; Zbl 1016.55010)] introduced the notion of abelian model categories as bicomplete abelian categories possessing a compatible model structure. His most wonderful result, which is now known as \textit{Hovey's correspondence}, says that there is a one-to-one correspondence between abelian model ...
Di, Zhenxing +3 more
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Cosupport for Tensor Triangulated Categories
Bulletin of the Iranian Mathematical SocietyBy constructing local homology and cohomology functors on a triangulated category \(\mathcal{T}\), \textit{D. Benson} et al. [Ann. Sci. Éc. Norm. Supér. (4) 41, No. 4, 575--621 (2008; Zbl 1171.18007); J. Reine Angew. Math. 673, 161--207 (2012; Zbl 1271.18012)] proposed a new method for defining the notions of support and cosupport for objects in ...
Chen, Tao, Yang, Xiaoyan
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2010
Over the last few decades triangulated categories have become increasingly important, to the extent that they can now be viewed as a unifying theory underlying major parts of modern mathematics. This 2010 collection of survey articles, written by leading experts, covers fundamental aspects of triangulated categories, as well as applications in ...
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Over the last few decades triangulated categories have become increasingly important, to the extent that they can now be viewed as a unifying theory underlying major parts of modern mathematics. This 2010 collection of survey articles, written by leading experts, covers fundamental aspects of triangulated categories, as well as applications in ...
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Uniqueness of Enhancements of Triangulated Categories
We survey recent progress on uniqueness of enhancements of triangulated categories, and existence of lifts of exact functors. We focus on the geometric context.Canonaco Alberto +2 more
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