Gluing approximable triangulated categories

Author: yckw

August undefined, 2024

Webcategory can be thought of as a category where many objects are the limits of their Fourier expansions. And then come two types of theorems: (1) theorems providing examples, meaning showing that some category you might naturally want to look at is approximable, and (2) general structure theorems about approximable triangulated http://math.stanford.edu/~conrad/diffgeomPage/handouts/gluing.pdf

Preresolving categories and derived equivalences

WebA triangulated category is \emph{approximable} if this modified procedure is possible. Not surprisingly this has proved a powerful tool. For example: the fact that the derived category of a quasi compact, separated scheme is approximable has led to major improvements on old theorems due to Bondal, Van den Bergh and Rouquier. In this article we ... Webcategories by gluing t-structures via recollements. Our results on gluing partial silting sets are based on a technical criterion (theorem 6.3), which allows to glue partial silting sets T X and T Y in triangulated categories X and Y with respect to a recollement (Y≡D≡X). Conditions of theorem 6.3 are easier to check when T X and T christopher molineux

Finite approximations as a tool for studying triangulated categories

WebRalph M. Kaufmann – Feynman categories and representation theory ; Mark Kleiner – Preprojective roots and graph monoids of Coxeter groups ; Amnon Neeman – Approximable triangulated categories ; Sebastian Posur – Methods of constructive category theory WebAmnon Neeman (ANU) Approximable Triangulated Categories 2 September 202417/104. Heuristic, continued We will soon be assuming that the metric is non-archimedean. Replacing the metric by an equivalent (if necessary), we may also assume our metric takes values in the set of rational numbers of the form WebNov 18, 2024 · And then come two types of theorems: (1) theorems providing examples, meaning showing that some category you might naturally want to look at is approximable, and (2) general structure theorems about approximable triangulated categories. And what makes it all interesting is (3) applications. These turn out to include the proof of a … getty and associates

Triangulated categories via metric techniques, 3

WebJun 19, 2024 · Approximable triangulated categories. In this survey we present the relatively new concept of \emph {approximable triangulated categories.} We will show that the definition is natural, that it leads to powerful new results, and that it throws new light on old, familiar objects. In particular: a recent theorem says that the category is ... WebJul 13, 2024 · The authors believe that the weight structure view on this matter can be useful since weight structures ‘‘glue’’ and ‘‘localize’’ well (one may say that ‘‘weight structures localize ... The writing of this note was motivated by the nice properties of approximable triangulated categories established in . So now we will say a ... christopher molineWebNov 18, 2024 · And then come two types of theorems: (1) theorems providing examples, meaning showing that some category you might naturally want to look at is … christopher molinaro obituary

"WebGLUING RESTRICTED NERVES OF ∞-CATEGORIES 3 We say that a subset E⊆ Ar(C) is admissible (Deﬁnition 3.18) if Econtains every identity morphism, E is stable under … " - Gluing approximable triangulated categories

Gluing approximable triangulated categories

WebGluing approximable triangulated categories (with Amnon Neeman and Bregje Pauwels)- arXiv: 1806.05342, 18 pages, preprint. 9. Transfer of A-in nity structures to projective resolutions - arXiv:1801.08933, 20 pages, preprint. 8. Strictly unital A-in nity algebras - Journal of Pure and Applied Algebra, 222 (12), 4099-4125. 7. Golod rings and ... WebGiven a bounded-above cochain complex of modules over a ring, it is standard to replace it by a projective resolution, and it is classical that doing so can be very useful. Recently, a modified version of this was introduced in triangulated categor

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WebLet Tbe a triangulated category, possibly with coproducts, let A⊂Tbe ... Then the category D qc,Z (X) isweakly approximable. 3 Let X be a quasicompact, separated scheme. Then the category D qc(X) isapproximable. ... gluing … WebJun 14, 2024 · A triangulated category is approximable if this modified procedure is possible. Not surprisingly this has proved a powerful tool. For example: the fact that the derived category of a quasi compact, separated scheme is approximable has led to major improvements on old theorems due to Bondal, Van den Bergh and Rouquier. In this …

WebA triangulated category is emph{approximable} if this modified procedure is possible. Not surprisingly this has proved a powerful tool. For example: the fact that the derived category of a quasi compact, separated scheme is approximable has led to major improvements on old theorems due to Bondal, Van den Bergh and Rouquier. WebGluing Approximable Triangulated Categories. Given a bounded-above cochain complex of modules over a ring, it is standard to replace it by a projective resolution, and it is classical that doing so can be very useful. Recently, a modified version of this was introduced in triangulated categories other than the derived category of a ring.

http://export.arxiv.org/abs/1806.05342v2 Webtriangulated) categories. An example of a limit is gluing: imagine that you want to glue the 1/triangulated category of quasi-coherent sheaves on a scheme Xfrom an a ne cover. Below we will explain why just the above operation of gluing along an open cover unavoidably appears in the theory that we are trying to build.

WebAug 26, 2024 · Approximable triangulated categories. This talk will introduce a new machine: approximable triangulated categories. The applications so far are: (1) Proofs of conjectures of Bondal, Van den Bergh and Rouquier about strong generation, and (2) A really short, one-page proof of Serre’s old GAGA theorem. In my ARC application I made …

Webby (reasonable) equivalence relations. In this handout we explain some general gluing procedures, and we give some examples. Since the Hausdorﬀ property of a space is … getty and townend praise classicsWebGLUING APPROXIMABLE TRIANGULATED CATEGORIES JESSE BURKE, AMNON NEEMAN, AND BREGJE PAUWELS Abstract. Given a bounded-above cochain complex … getty and dubayWebA triangulated category is \emph{approximable} if this modified procedure is possible. Not surprisingly this has proved a powerful tool. For example: the fact that the derived … getty and associates waWebrecollement of triangulated categories Roo /Soo /T with Rand Tapproximable. Assume further that the category Sis compactly generated, and any compact object H ∈Shas the property that Hom H,H[i] = 0 for i ≫0. Then the category Sis also approximable. Amnon Neeman (ANU) Triangulated categories via metric techniques, 3 24 March 20248/126 getty angels we have heard on high lyricsWebApr 26, 2024 · Idea. Any (infinity,1)-category C C can be flattened, by ignoring higher morphisms, into a 1-category ho (C) ho(C) called its homotopy category.The notion of a triangulated structure is designed to capture the additional structure canonically existing on ho (C) ho(C) when C C has the property of being stable.This structure can be described … getty and newsomWebGluing approximable triangulated categories with Amnon Neeman and Bregje Pauwels. Submitted, 18 pages. Transfer of A-infinty structures to projective resolutions Preprint, 20 … christopher molanderWebJun 14, 2024 · A triangulated category is \emph{approximable} if this modified procedure is possible. Not surprisingly this has proved a powerful tool. For example: the fact that the … getty and townend