Realization functors in algebraic triangulated categories

2024/12/10 by Janina C. Letz, Letz, Janina C., Julia Sauter +1
Mathematics · #18G80 18G35 #Advanced Topics in Algebra #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2412.07455

openalex publication_date 2024/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let T be an algebraic triangulated category and C an extension-closed subcategory with Hom(C, Σ^<0 C)=0. Then C has an exact structure induced from exact triangles in T. Keller and Vossieck say that there exists a triangle functor D^b(C) → T extending the inclusion C ⊆ T. We provide the missing details for a complete proof.

Related

• Localization of triangulated categories with respect to extension-closed subcategories
• Representable triangulated functors in terms of semiorthogonal decompositions
• Definable functors between triangulated categories
• Adjoint functors and triangulated categories
• External triangulation of the homotopy category of exact quasi-category