The categories \mathcal T^c and \mathcal T^b_c determine each other

2018/06/18 by Amnon Neeman, Neeman, Amnon
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary 18E30 #secondary 18G55

paper · pdf · doi:10.48550/arxiv.1806.06471

openalex publication_date 2018/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given an essentially small triangulated category it is possible to give a metric on it, to complete it with respect to the metric, and to look at the subcategory of objects in the completion which are compactly supported with respect to the metric. The main theorem says that this procedure produces a new triangulated category. And then we give examples: for example we learn that it is possible, for suitable choices of metrics, to produce the categories D^b(R-mod) and K^b(R-proj) out of each other.

Citations

• Completing perfect complexes

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