We exploit the equivalence between t-structures and normal torsion theories on a stable ∞-category to show how a few classical topics in the theory of triangulated categories, i.e., the characterization of bounded t-structures in terms of their hearts, their associated cohomology functors, semiorthogonal decompositions, and the theory of tiltings, as well as the more recent notion of Bridgeland’s slicings, are all particular instances of a single construction, namely, the tower of a morphism associated with a J-slicing of a stable ∞-category Open image in new window , where J is a totally ordered set equipped with a monotone ℤ-action.

Hearts and towers in stable infinity-categories $$infty $$ ∞ -categories / Fiorenza, Domenico; Loregian, Fosco; Marchetti, Giovanni Luca. - In: JOURNAL OF HOMOTOPY AND RELATED STRUCTURES. - ISSN 2193-8407. - (2019). [10.1007/s40062-019-00237-0]

Hearts and towers in stable infinity-categories $$infty $$ ∞ -categories

Fiorenza, Domenico;
2019

Abstract

We exploit the equivalence between t-structures and normal torsion theories on a stable ∞-category to show how a few classical topics in the theory of triangulated categories, i.e., the characterization of bounded t-structures in terms of their hearts, their associated cohomology functors, semiorthogonal decompositions, and the theory of tiltings, as well as the more recent notion of Bridgeland’s slicings, are all particular instances of a single construction, namely, the tower of a morphism associated with a J-slicing of a stable ∞-category Open image in new window , where J is a totally ordered set equipped with a monotone ℤ-action.
Stable ∞-categories; triangulated categories; t-structures; tilting theory; semiorthogonal decompositions; stability conditions on triangulated categories
01 Pubblicazione su rivista::01a Articolo in rivista
Hearts and towers in stable infinity-categories $$infty $$ ∞ -categories / Fiorenza, Domenico; Loregian, Fosco; Marchetti, Giovanni Luca. - In: JOURNAL OF HOMOTOPY AND RELATED STRUCTURES. - ISSN 2193-8407. - (2019). [10.1007/s40062-019-00237-0]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1286427
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