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Classifying space of subcategories and its application

2017/09/09 by Yong Liu, Liu, Yong
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1709.02982

openalex publication_date 2017/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a collection of subcategories satisfying a fixed set of conditions, for example thick subcategories of a triangulated category, we define a topological space called classifying space of subcategories. We show that this space classifies various prime subcategories in the sense that they bijectively correspond to the closed subsets of the classifying space. Many well-known results of subcategory classification fit into this framework. An example which cannot be classified by a topological space in the above sense is also given.

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