Year: 2026
Type: preprint
Abstract: Let $(\mathscr{C}, \mathbb{E}, \mathfrak{s})$ be a weakly idempotent complete extriangulated category, and let $ξ_1\subseteqξ_2$ be proper classes of $\mathbb{E}$-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 $\mathcal{M}_m$ 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 $\mathcal{M}_m$ 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.
Source: arXiv (Cornell University)
Authors: Ren, Junpeng, Fu, Xianhui
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213344697