Derived, coderived, and contraderived categories of locally presentable abelian categories

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00545361" target="_blank" >RIV/67985840:_____/22:00545361 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216208:11320/22:10452303

Výsledek na webu

<a href="https://doi.org/10.1016/j.jpaa.2021.106883" target="_blank" >https://doi.org/10.1016/j.jpaa.2021.106883</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jpaa.2021.106883" target="_blank" >10.1016/j.jpaa.2021.106883</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Derived, coderived, and contraderived categories of locally presentable abelian categories

Popis výsledku v původním jazyce

For a locally presentable abelian category B with a projective generator, we construct the projective derived and contraderived model structures on the category of complexes, proving in particular the existence of enough homotopy projective complexes of projective objects. We also show that the derived category D(B) is generated, as a triangulated category with coproducts, by the projective generator of B. For a Grothendieck abelian category A, we construct the injective derived and coderived model structures on complexes. Assuming Vopěnka’s principle, we prove that the derived category D(A) is generated, as a triangulated category with products, by the injective cogenerator of A. We also define the notion of an exact category with an object size function and prove that the derived category of any such exact category with exact κ-directed colimits of chains of admissible monomorphisms has Hom sets. Hence the derived category of any locally presentable abelian category has Hom sets.

Název v anglickém jazyce

Derived, coderived, and contraderived categories of locally presentable abelian categories

Popis výsledku anglicky

For a locally presentable abelian category B with a projective generator, we construct the projective derived and contraderived model structures on the category of complexes, proving in particular the existence of enough homotopy projective complexes of projective objects. We also show that the derived category D(B) is generated, as a triangulated category with coproducts, by the projective generator of B. For a Grothendieck abelian category A, we construct the injective derived and coderived model structures on complexes. Assuming Vopěnka’s principle, we prove that the derived category D(A) is generated, as a triangulated category with products, by the injective cogenerator of A. We also define the notion of an exact category with an object size function and prove that the derived category of any such exact category with exact κ-directed colimits of chains of admissible monomorphisms has Hom sets. Hence the derived category of any locally presentable abelian category has Hom sets.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA20-13778S" target="_blank" >GA20-13778S: Symetrie, duality a aproximace v derivované algebraické geometrii a teorii reprezentací</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Journal of Pure and Applied Algebra

ISSN

0022-4049

e-ISSN

1873-1376

Svazek periodika

226

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

39

Strana od-do

106883

Kód UT WoS článku

000703984500021

EID výsledku v databázi Scopus

2-s2.0-85114424531