Extriangulated categories
WebOct 1, 2024 · As a simultaneous generalization and enhancement of the Auslander-Reiten theory in exact categories and triangulated categories, recently, Iyama, Nakaoka and Palu [13] investigated the Auslander-Reiten theory in extriangulated categories. They gave two different sets of sufficient conditions in the extriangulated category so that the existence ... WebJul 10, 2024 · Extriangulated categories were introduced by Nakaoka and Palu to give a unification of properties in exact categories and extension-closed subcategories of triangulated categories. A notion of tilting pairs in an extriangulated category is introduced in this paper. We give a Bazzoni characterization of tilting pairs in this setting. We also …
Extriangulated categories
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WebExtriangulated categories were introduced by Nakaoka and Palu as a simultaneous generalization of exact categories and triangulated categories. In this paper, we show … WebJan 1, 2005 · Second, we develop a theory of stratifying systems in extriangulated categories. We define projective stratifying systems and show that every stratifying …
http://www.tac.mta.ca/tac/volumes/34/8/34-08.pdf WebDec 1, 2024 · In this article, let us discuss about localizations of extriangulated categories. As for the localizations which involve abelian/exact/triangulated categories, the following are known in the literature. (i) Serre quotient of an abelian category [5]. (ii) Verdier quotient of a triangulated category [17]. (iii)
Web2-Calabi-Yau extriangulated category is cluster-tilting, see Theorem4.3. 2. Preliminaries Throughout the paper, when we say that C is a category, we always assume that C is an additive category. All subcategories of a category C are full subcategories and closed under isomorphisms. For any object X2C, we denote by addXthe subcategory of C WebMar 15, 2024 · In n-Exangulated Categories (I), we introduced the notion of n-exangulated categories for each positive integer n.It is not only a higher dimensional analogue of …
WebNov 15, 2024 · Recently, Nakaoka and Palu introduced a notion of extriangulated categories. This is a unification of exact categories and triangulated categories. In this …
WebMar 15, 2024 · Recently, Nakaoka and Palu ( [20]) formalized the notion of extriangulated categories as a simultaneous generalization of exact categories and triangulated categories. Moreover, they introduced cotorsion pairs in an extriangulated category. mst course offeringsWebMar 13, 2024 · extriangulated categories and b ehaviour of those under n atural operations. In Section 3 , we introduce 0-Auslander extriangulated categories and prove … mst crawler bodyWebJan 7, 2024 · The index in 2-Calabi-Yau categories was recently interpreted by Padrol, Palu, Pilaud, and Plamondon in terms of extriangulated categories. In joint work with Amit Shah, we generalise the extriangulated viewpoint and define the index of an object of a triangulated category with respect to a rigid subcategory. ms tc rcaWebFeb 1, 2024 · In [27], Nakaoka and Palu introduced the notion of externally triangulated categories (extriangulated categories for short) as a simultaneous generalization of exact categories and... mst crawlerWebAug 16, 2024 · First, we introduce notions of subobjects, simple objects and composition series relative to the extriangulated structure in order to define a Jordan-Hölder … mstc property auctionWebApr 4, 2024 · We give a classification of substructures (= closed subbifunctors) of a given skeletally small extriangulated category by using the category of defects, in a similar … mstc raipur officeWebThe extriangulated categories which also have an exact or triangulated structure have been characterised. The extriangulated categories which are exact categories are … how to make lipstick with eyeshadow