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
SN - 0001-8708
VL - 357
JO - Advances in Mathematics
JF - Advances in Mathematics
M1 - 106826
ER -