A triangulated category without models
Fernando Muro
TL;DR
This paper constructs a specific triangulated category that cannot be realized as a stable category of a Frobenius category or as a subcategory of a stable model category's homotopy category, challenging existing assumptions.
Contribution
It provides a counterexample of a triangulated category that defies common model-based realizations, highlighting limitations in current categorical frameworks.
Findings
Existence of a triangulated category without models
Counterexample to model-based realizations of triangulated categories
Challenges assumptions about triangulated category representations
Abstract
We exhibit a triangulated category which is neither the stable category of a Frobenius category nor a full triangulated subcategory of the homotopy category of a stable model category.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra