Model categories of quiver representations

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Standard

Model categories of quiver representations. / Holm, Henrik; Jørgensen, Peter.

I: Advances in Mathematics, Bind 357, 106826, 2019.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Holm, H & Jørgensen, P 2019, 'Model categories of quiver representations', Advances in Mathematics, bind 357, 106826. https://doi.org/10.1016/j.aim.2019.106826

APA

Holm, H., & Jørgensen, P. (2019). Model categories of quiver representations. Advances in Mathematics, 357, [106826]. https://doi.org/10.1016/j.aim.2019.106826

Vancouver

Holm H, Jørgensen P. Model categories of quiver representations. Advances in Mathematics. 2019;357. 106826. https://doi.org/10.1016/j.aim.2019.106826

Author

Holm, Henrik ; Jørgensen, Peter. / Model categories of quiver representations. I: Advances in Mathematics. 2019 ; Bind 357.

Bibtex

@article{a606d7d3fd4842a884901c25f60dd60f,
title = "Model categories of quiver representations",
abstract = "Gillespie's Theorem gives a systematic way to construct model category structures on C(M), the category of chain complexes over an abelian category M. We can view C(M) as the category of representations of the quiver ⋯→2→1→0→−1→−2→⋯ with the relations that two consecutive arrows compose to 0. This is a self-injective quiver with relations, and we generalise Gillespie's Theorem to other such quivers with relations. There is a large family of these, and following Iyama and Minamoto, their representations can be viewed as generalised chain complexes. Our result gives a systematic way to construct model category structures on many categories. This includes the category of N-periodic chain complexes, the category of N-complexes where ∂N=0, and the category of representations of the repetitive quiver ZAn with mesh relations.",
keywords = "Abelian model categories, Chain complexes, Cotorsion pairs, Gillespie's and Hovey's Theorems, N-complexes, Periodic chain complexes",
author = "Henrik Holm and Peter J{\o}rgensen",
year = "2019",
doi = "10.1016/j.aim.2019.106826",
language = "English",
volume = "357",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press",

}

RIS

TY - JOUR

T1 - Model categories of quiver representations

AU - Holm, Henrik

AU - Jørgensen, Peter

PY - 2019

Y1 - 2019

N2 - Gillespie's Theorem gives a systematic way to construct model category structures on C(M), the category of chain complexes over an abelian category M. We can view C(M) as the category of representations of the quiver ⋯→2→1→0→−1→−2→⋯ with the relations that two consecutive arrows compose to 0. This is a self-injective quiver with relations, and we generalise Gillespie's Theorem to other such quivers with relations. There is a large family of these, and following Iyama and Minamoto, their representations can be viewed as generalised chain complexes. Our result gives a systematic way to construct model category structures on many categories. This includes the category of N-periodic chain complexes, the category of N-complexes where ∂N=0, and the category of representations of the repetitive quiver ZAn with mesh relations.

AB - Gillespie's Theorem gives a systematic way to construct model category structures on C(M), the category of chain complexes over an abelian category M. We can view C(M) as the category of representations of the quiver ⋯→2→1→0→−1→−2→⋯ with the relations that two consecutive arrows compose to 0. This is a self-injective quiver with relations, and we generalise Gillespie's Theorem to other such quivers with relations. There is a large family of these, and following Iyama and Minamoto, their representations can be viewed as generalised chain complexes. Our result gives a systematic way to construct model category structures on many categories. This includes the category of N-periodic chain complexes, the category of N-complexes where ∂N=0, and the category of representations of the repetitive quiver ZAn with mesh relations.

KW - Abelian model categories

KW - Chain complexes

KW - Cotorsion pairs

KW - Gillespie's and Hovey's Theorems

KW - N-complexes

KW - Periodic chain complexes

UR - http://www.scopus.com/inward/record.url?scp=85072704801&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2019.106826

DO - 10.1016/j.aim.2019.106826

M3 - Journal article

AN - SCOPUS:85072704801

VL - 357

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

M1 - 106826

ER -

ID: 229101378