Abstract tilting theory for quivers and related categories

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10383382" target="_blank" >RIV/00216208:11320/18:10383382 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.2140/akt.2018.3.71" target="_blank" >https://doi.org/10.2140/akt.2018.3.71</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.2140/akt.2018.3.71" target="_blank" >10.2140/akt.2018.3.71</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Abstract tilting theory for quivers and related categories

Popis výsledku v původním jazyce

We generalize the construction of reflection functors from classical representation theory of quivers to arbitrary small categories with freely attached sinks or sources. These reflection morphisms are shown to induce equivalences between the corresponding representation theories with values in arbitrary stable homotopy theories, including representations over fields, rings or schemes as well as differential-graded and spectral representations. Specializing to representations over a field and to specific shapes, this recovers derived equivalences of Happel for finite, acyclic quivers. However, even over a field our main result leads to new derived equivalences, for example, for not necessarily finite or acyclic quivers. Our results rely on a careful analysis of the compatibility of gluing constructions for small categories with homotopy Kan extensions and homotopical epimorphisms, and on a study of the combinatorics of amalgamations of categories.

Název v anglickém jazyce

Abstract tilting theory for quivers and related categories

Popis výsledku anglicky

We generalize the construction of reflection functors from classical representation theory of quivers to arbitrary small categories with freely attached sinks or sources. These reflection morphisms are shown to induce equivalences between the corresponding representation theories with values in arbitrary stable homotopy theories, including representations over fields, rings or schemes as well as differential-graded and spectral representations. Specializing to representations over a field and to specific shapes, this recovers derived equivalences of Happel for finite, acyclic quivers. However, even over a field our main result leads to new derived equivalences, for example, for not necessarily finite or acyclic quivers. Our results rely on a careful analysis of the compatibility of gluing constructions for small categories with homotopy Kan extensions and homotopical epimorphisms, and on a study of the combinatorics of amalgamations of categories.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

ANNALS OF K-THEORY

ISSN

2379-1683

e-ISSN

—

Svazek periodika

3

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

54

Strana od-do

71-124

Kód UT WoS článku

000432712300004

EID výsledku v databázi Scopus

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