A functorial approach to rank functions on triangulated categories
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00586333" target="_blank" >RIV/67985840:_____/24:00586333 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1515/crelle-2024-0009" target="_blank" >https://doi.org/10.1515/crelle-2024-0009</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/crelle-2024-0009" target="_blank" >10.1515/crelle-2024-0009</a>
Alternative languages
Result language
angličtina
Original language name
A functorial approach to rank functions on triangulated categories
Original language description
We study rank functions on a triangulated category C via its abelianisation mod C. We prove that every rank function on C can be interpreted as an additive function on mod C. As a consequence, every integral rank function has a unique decomposition into irreducible ones. Furthermore, we relate integral rank functions to a number of important concepts in the functor category Mod C. We study the connection between rank functions and functors from C to locally finite triangulated categories, generalising results by Chuang and Lazarev. In the special case C D T c for a compactly generated triangulated category T, this connection becomes particularly nice, providing a link between rank functions on C and smashing localisations of T . In this context, any integral rank function can be described using the composition length with respect to certain endofinite objects in T . Finally, if C D per.A/ for a differential graded algebra A, we classify homological epimorphisms A ! B with per.B / locally finite via special rank functions which we call idempotent.
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
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal für die Reine und Angewandte Mathematik: Crelles journal
ISSN
0075-4102
e-ISSN
1435-5345
Volume of the periodical
811
Issue of the periodical within the volume
May
Country of publishing house
DE - GERMANY
Number of pages
47
Pages from-to
135-181
UT code for WoS article
001185764400001
EID of the result in the Scopus database
2-s2.0-85188192061