t-Structures on stable derivators and Grothendieck hearts

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10471932" target="_blank" >RIV/00216208:11320/23:10471932 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=P7nyF9.kQ9" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=P7nyF9.kQ9</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.aim.2023.109139" target="_blank" >10.1016/j.aim.2023.109139</a>

Jazyk výsledku

angličtina

Název v původním jazyce

t-Structures on stable derivators and Grothendieck hearts

Popis výsledku v původním jazyce

We prove that, given any strong and stable derivator and a t-structure in its base triangulated category D, the t structure canonically lifts to all the (coherent) diagram categories and each incoherent diagram in the heart uniquely lifts to a coherent one. We use this to show that the t structure being compactly generated implies that the coaisle is closed under directed homotopy colimits which, in turn, implies that the heart is an (Ab.5) Abelian category. If, moreover, D is a well-generated algebraic or topological triangulated category, then the heart of any accessibly embedded (in particular, compactly generated) t-structure has a generator. As a consequence, it follows that the heart of any compactly generated t-structure of a well generated algebraic or topological triangulated category is a Grothendieck Abelian category. &amp; COPY; 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons .org /licenses /by -nc -nd /4 .0/).

Název v anglickém jazyce

t-Structures on stable derivators and Grothendieck hearts

Popis výsledku anglicky

We prove that, given any strong and stable derivator and a t-structure in its base triangulated category D, the t structure canonically lifts to all the (coherent) diagram categories and each incoherent diagram in the heart uniquely lifts to a coherent one. We use this to show that the t structure being compactly generated implies that the coaisle is closed under directed homotopy colimits which, in turn, implies that the heart is an (Ab.5) Abelian category. If, moreover, D is a well-generated algebraic or topological triangulated category, then the heart of any accessibly embedded (in particular, compactly generated) t-structure has a generator. As a consequence, it follows that the heart of any compactly generated t-structure of a well generated algebraic or topological triangulated category is a Grothendieck Abelian category. &amp; COPY; 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons .org /licenses /by -nc -nd /4 .0/).

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10101 - Pure mathematics

Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Advances in Mathematics

ISSN

0001-8708

e-ISSN

1090-2082

Svazek periodika

429

Číslo periodika v rámci svazku

15 September 2023

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

70

Strana od-do

109139

Kód UT WoS článku

001032944300001

EID výsledku v databázi Scopus

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