Tensor triangulated category

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August undefined, 2024

Weba "triangulated category of triangulated functors between triangulated categories" or a tensor product. Problems arise essentially from the failure of functoriality of mapping cones. The solution to this issue is to consider enhancements of triangulated categories: namely, viewing them as shadows WebA triangulated category is an additive category with an additive auto-equivalence called a translation (or shift) functor, and a class of distinguished triangles satisfying various axioms. Learn more… Top users Synonyms 179 questions Newest Active Filter 1 vote 0 answers 30 views Product, coproduct, and convolution of chain complexes

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Web26 Sep 2014 · Since {\underline {\sf {CM}} k (G\propto\mathcal {P})} is also tensor triangulated, we compute its spectrum as well. These spectra are used to classify tensor … ex fleet cars for sale victoria

Tensor triangulated categories associated to schemes and their …

Web2 Jul 2013 · We prove that the category of modules over a separable ring object in a tensor triangulated category admits a unique structure of triangulated category which is compatible with the original one ... Webtensor triangulated category K, since Spc(K) is the universal locus for supports, the general version of Thomason’s Theorem should involve the following construction: Spc(K) ⊃ Y … WebThe goal of this note is to spell out the (apparently well-known and intuitively clear) notion of an abelian category over a stack. In the future we will discuss the (much less evident) notion, when instead of an abelian category one considers a triangulated one. ex fleet vans for sale north east

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Webtriangulated categories, and a complete description of the spectrum is equivalent to a classiﬁcation of the thick -ideals in the category. For the remainder of the introduction, we assume K is tensor-triangulated and nice (say, Spc.K/is noetherian or K satisﬁes Krull–Schmidt). If A is a separable ring in K, the Eilenberg–Moore category ... WebThe tensor product of any A-module with a projective is projective, and hence the same is true of modules of ﬁnite projective dimension. Thus GProj(A)isatensor triangulated category and the approximation functor is a tensor functor. The ideal (τ)inA is primitively generated, so the quotient k[t]/(tp) inherits a ex fleet trackingWebCategory : Finite groups Languages : en Pages : 372. Download Book. Book Description. Representation Theory I. Proceedings of the Fourth International Conference on Representations of Algebras, held in Ottawa, Canada, August 16-25, 1984 PDF Download Are you looking for read ebook online? Search for your book and save it on your Kindle device ... ex fleet pickups for sale

"Web2 RYO TAKAHASHI triangulated category, that is, a triangulated category Tequipped with symmetric tensor product ⊗and unit object 1l.A (thick tensor) ideal of Tis by deﬁnition a thick subcategory of Twhich is closed under the action of Tby ⊗.A proper ideal Pof Tis called prime if it satisﬁes: X ⊗Y ∈P=⇒X ∈Por Y ∈P. Prime ideals of tensor triangulated … " - Tensor triangulated category

Tensor triangulated category

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Web28 Jun 2024 · The tensor structure is the one we have met before, through monoidal categories, but the triangulated structure we have not yet explored in our mathematical endeavors on this blog. So, lets change that fact. To justify it’s name, triangulated … Webadditive category and the projection is an additive functor. Now suppose that T is a triangulated category and that F is a triangle functor. Is there a triangulated structure on the orbit category such that the projection functor becomes a triangle functor? One can show that in general, the answer is negative. A closer look at the situation ...

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Web10.3. Remark. If T is a non-closed tensor-triangulated category then Tdis a rigid essentially small tensor-triangulated subcategory of T. 10.4. Remark. If T is a rigidly-compactly generated tensor-triangulated category in the usual sense then T d= Tc. Nevertheless, we will often write T when emphasizing dualizability over compactness. WebDeﬁnition 3.1. Let Tbe a triangulated category. A full subcategory Xof Tis called thick if it is closed under cones, direct summands and the action of Σ and Σ−1, i.e. it is a triangulated subcategory of Tclosed under direct summands. The set of thick subcategories of an essentially small triangulated category Tforms a complete lattice

Webunderlying tensor triangulated category (hT )⊗. Deﬁnition3.6 LetT ⊗ beatt-∞-category.Asupport forT ⊗ isapair(L,s)ofadistributive lattice L and a function s: T → L satisfying the following: (0) The function s takes the same values on equivalent objects. Hence we can evaluate s(C) even if C is only determined up to equivalence. WebTo do so, users select a point in a triangulated dimensionally-reduced plot. The selected setting is found by barycentric interpolation. Kerr et al. tested sliders against a gallery-based system in a user study. The latter worked such that the user selects two dimensions and then sees a 5 × 5 gallery of the output with the two parameters step ...

Web11 Apr 2024 · We compare the homological support and tensor triangular support for ‘big’ objects in a rigidly-compactly generated tensor triangulated category. We prove that the comparison map from the ... WebStack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchange

WebWe have the functor # (see II, x2.5) on the category of triangulated tensor categories, where A# is the pseudo-abelian hull of a category A. Applying (7.2.5) again, it su ces to show that, if Ais a tensor category having a duality involution ( )D, if Ais an object of A, and if Bis the summand of Ain A# corresponding to an idempotent endomorphism

WebOn the surjectivity of the map of spectra associated to a tensor-triangulated functor. Bull. Lond. Math. Soc. 50 (3):487-495, 2024, DOI 10.1112/blms.12158, zbl 1436.18010, MR3829735, arxiv 1706.03291. [Balmer and Favi (2011)]. P. Balmer and G. Favi. Generalized tensor idempotents and the telescope conjecture. Proc. exflow attestWeb25 Mar 2024 · We say that a $\V$-enriched category $\C$ is tensored over $\V$ if there is a functor (usually also denoted $\otimes$, but for which I'll use $\boxtimes$ for clarity here) … bt home hub lights meaningWeb10 Apr 2024 · As one of the most important components of urban space, an outdated inventory of road-side trees may misguide managers in the assessment and upgrade of urban environments, potentially affecting urban road quality. Therefore, automatic and accurate instance segmentation of road-side trees from urban point clouds is an … exflow bcWeb19 Apr 2024 · [Submitted on 19 Apr 2024] Noncommutative tensor triangulated categories and coherent frames Vivek Mohan Mallick, Samarpita Ray We develop a point-free … bt home hub manualWeb21 May 2024 · Precisely, if a tensor triangulated category has a semi-orthogonal decomposition, then its spectrum is homeomorphic to the disjoint copies of the spectra … exflow cloudWeb20 Oct 2004 · In its most modernized form, the central theme under inspection is the classification of localizing tensor-ideals of a rigidlycompactly generated tensor … exflow apiWebTENSOR TRIANGULATED CATEGORY STRUCTURES IN THE DERIVED CATEGORY OF A VARIETY WITH BIG (ANTI-)CANONICAL BUNDLE ANGEL TOLEDO Abstract. Let X be a … bt home hub manager home