Abstract tilting theory for quivers and related categories
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Abstract tilting theory for quivers and related categories
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
ANNALS OF K-THEORY
ISSN
2379-1683
e-ISSN
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Volume of the periodical
3
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
54
Pages from-to
71-124
UT code for WoS article
000432712300004
EID of the result in the Scopus database
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