Mixing Extriangulated Model Structures
Abstract
Let (𝒞, 𝔼, s) be a weakly idempotent complete extriangulated category, and let ξ1⊆ξ2 be proper classes of 𝔼-triangles. We prove an analogue of Cole's mixing theorem in this setting: two compatible admissible model structures, relative to ξ1 and ξ2 respectively, give rise to a mixed admissible model structure ℳm relative to ξ1, which has the trivial objects of the second model structure and the fibrant (or cofibrant) objects of the first. We also describe the cofibrant objects of ℳm explicitly in terms of the two original model structures. For exact categories this recovers the mixing theorem for exact model structures, and for triangulated categories it applies to proper classes of triangles; we give a non-degenerate example on the homotopy category of a quasi-Frobenius ring.
Related
- Exceptional model structures and the induced extriangulated categories
- Extriangulated ideal quotients and d-Auslander categories
- A refined multiplication formula in 2-Calabi-Yau Frobenius extriangulated categories
- Extriangulated ideal quotients, with applications to cluster theory and gentle algebras
- Relative quasi-Gorenstein homological dimensions in extriangulated categories
BibTeX
@misc{ren2026mixing,
title = {{Mixing Extriangulated Model Structures}},
author = {Junpeng Ren and Xianhui Fu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.15653},
eprint = {2609.15653},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15653},
}
RIS
TY - UNPB
TI - Mixing Extriangulated Model Structures
AU - Junpeng Ren
AU - Xianhui Fu
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2609.15653
UR - https://arxiv.org/abs/2609.15653
AB - Let (𝒞, 𝔼, s) be a weakly idempotent complete extriangulated category, and let ξ_1⊆ξ_2 be proper classes of 𝔼-triangles. We prove an analogue of Cole's mixing theorem in this setting: two compatible admissible model structures, relative to ξ_1 and ξ_2 respectively, give rise to a mixed admissible model structure ℳ_m relative to ξ_1, which has the trivial objects of the second model structure and the fibrant (or cofibrant) objects of the first. We also describe the cofibrant objects of ℳ_m explicitly in terms of the two original model structures. For exact categories this recovers the mixing theorem for exact model structures, and for triangulated categories it applies to proper classes of triangles; we give a non-degenerate example on the homotopy category of a quasi-Frobenius ring.
ER -