Enhanced triangulated categories
WebJun 18, 2024 · Enhanced ˝nite triangulated categories 743 Most triangulated categories appearing in the literature are born with an enhancement. This theorem is still interesting … WebOct 18, 2007 · In general, for any A ∞ -category A , we can construct the enhanced triangulated category T r(A ) by using Bondal-Kapranov-Kontsevich construction [7, …
Enhanced triangulated categories
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WebMar 21, 2024 · Rina Anno, Sergey Arkhipov, Timothy Logvinenko. We define -structures -- algebras, coalgebras, modules, and comodules -- in an arbitrary monoidal DG category or bicategory by rewriting their definitions in terms of unbounded twisted complexes. We develop new notions of strong homotopy unitality and bimodule homotopy unitality to …
WebSep 3, 2013 · Download a PDF of the paper titled Tannaka duality for enhanced triangulated categories II: $t$-structures and homotopy types, by J.P.Pridham … WebIf Tis a small dg-enhanced triangulated category and D(T) is the derived category of right dg-modules over T, we say that an object M∈D(T) is homologically finite-dimensional if M(t) ∈Db(k), i.e., M(t) is bounded and finite-dimensional for any object t∈T(see Definition 3.1). The category Dfd(T) of homologically finite-dimensional ...
WebJul 1, 2010 · Abstract. The paper contains general results on the uniqueness of a DG enhancement for triangulated categories. As a consequence we obtain such … WebJun 18, 2024 · Enhanced ˝nite triangulated categories 743 Most triangulated categories appearing in the literature are born with an enhancement. This theorem is still interesting for nite triangulated categories for which an enhancement is known since it shows uniqueness up to Morita equivalence. The stable category mod.A/of nite-dimensional modules over a ...
WebMay 27, 2024 · H V is a genuine 2-catego ry whose 1-morphisms categories are triangulated and Karoubi- complete. In particular, it recovers all the combinatorics of the additiv e setting.
WebAug 22, 2024 · In past talks at this conference we have seen the definition of a triangulated category and some examples of familiar triangulated categories, including the homotopy category \(\mathscr {H}(R)\) and the derived category \(\mathscr {D}(R)\) of modules over some ring R.These categories are defined by applying certain constructions to the … storage sync service naming conventionWebMar 24, 2024 · Abstract. We lift Grothendieck–Verdier–Spaltenstein’s six functor formalism for derived categories of sheaves on ringed spaces over a field to differential graded enhancements. Our main tools come from enriched model category theory. Download to read the full article text. rosebery wing tippethill hospitalWebJun 18, 2024 · ENHANCED FINITE TRIANGULATED CATEGORIES - Volume 21 Issue 3. To save this article to your Kindle, first ensure [email protected] is added to … rosebery warehouseWebNov 15, 2024 · Toën [12] gave a construction of what he called derived Hall algebras for DG-enhanced triangulated categories satisfying certain finiteness conditions. Later, Xiao and Xu [13] showed that Toën's definition also applies to any triangulated categories satisfying certain finiteness conditions. They proved the associativity formulas of the ... rosebery weather tasmaniaWebWe observe that the resulting triangulated orbit categories provide many examples of triangulated categories with the Calabi-Yau property. These include the category of projective modules over a preprojective algebra of generalized Dynkin type in the sense of Happel-Preiser-Ringel [27], whose triangulated structure goes back to Auslander-Reiten’s rosebery weather 14 day forecastWebJul 2, 2024 · Abstract. Given a finite group action on a (suitably enhanced) triangulated category linear over a field, we establish a formula for the Hochschild cohomology of the … storage sync services vs azure file syncWeb[Knu02a, Appendix B] had suggested considering Db(E) as a triangulated category enhanced with a category of ‘true triangles’, to develop a theory of determinant functors for such enhanced triangulated categories, and to show that any determi-nant functor det: E →P extends to det: Db(E) →P in an essentially unique way for E additive or ... rosebery weather forecast