A functorial approach to rank functions on triangulated categories

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

A functorial approach to rank functions on triangulated categories

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

A functorial approach to rank functions on triangulated categories

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Journal für die Reine und Angewandte Mathematik: Crelles journal

ISSN

0075-4102

e-ISSN

1435-5345

Svazek periodika

811

Číslo periodika v rámci svazku

May

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

47

Strana od-do

135-181

Kód UT WoS článku

001185764400001

EID výsledku v databázi Scopus

2-s2.0-85188192061