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

Amnon Neeman

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

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arxiv 1806.06471 v2 pith:SSAJZKPP submitted 2018-06-18 math.CT

Amnon Neeman This is my paper · ORCID

classification math.CT

keywords metriccategoriescategorygivemathcalotherpossiblerespect

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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 $D^b(R-\text{mod})$ and $K^b(R-\text{proj})$ out of each other.

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Triangulated categories with a compact silting object, Brown-Comenetz duality and Brown representability theorems
math.RT 2026-02 conditional novelty 6.0 of 10

For triangulated categories with a compact silting object, the Brown–Comenetz duals of compact objects form a subcategory E, and the new intrinsic subcategory T_c^+ represents exactly the locally finite E-homological ...

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