Representability theorems via metric techniques

2025/04/16 by Kabeer Manali Rahul, Rahul, Kabeer Manali · 2 citations
Mathematics · #14A30 #18G80(primary) #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2504.11768

openalex publication_date 2025/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove new Brown representability theorems for triangulated categories using metric techniques as introduced in the work of Neeman. In the setting of algebraic geometry, this gives us new representability theorems for homological and cohomological functors on the bounded derived category of coherent sheaves. To prove this result, we introduce a generalisation of the notion of an approximable triangulated category.

Cited by

• Intrinsic homological algebra for triangulated categories
• Metric completions of triangulated categories from hereditary rings

Related

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• Metric completions of triangulated categories from finite dimensional algebras