Triangulated categories without models

Abstract

We exhibit examples of triangulated categories which are neither the stable category of a Frobenius category nor a full triangulated subcategory of the homotopy category of a stable model category. Even more drastically, our examples do not admit any non-trivial exact functors to or from these algebraic respectively topological triangulated categories.

10 pages

References in corpus (4)

• On triangulated orbit categories
• Algebraic versus topological triangulated categories
• A uniqueness theorem for stable homotopy theory
• Stable Infinity Categories

Cited by in corpus (16)

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• Separated monic representations II: Frobenius subcategories and RSS equivalences
• Singular extensions and triangulated categories
• Large self-injective rings and the generating hypothesis
• Notes on Triangulated Categories
• Quotient rings of $H{\mathbb{F}}_2\wedge H{\mathbb{F}}_2$
• Toward a strictification theorem for co-Segal categories
• Homotopy structures realizing algebraic kk-theory
• Triangulations of projective modules
• t-structures on stable infinity-categories
• Higher symmetries in abstract stable homotopy theories