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arXiv · 2407.17369

Metric completions of discrete cluster categories

Charley Cummings·Sira Gratz
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Abstract

Neeman shows that the completion of a triangulated category with respect to a good metric yields a triangulated category. We compute completions of discrete cluster categories with respect to metrics induced by internal t-structures. In particular, for a coaisle metric this yields a new triangulated category which can be interpreted as a topological completion of the associated combinatorial model. Moreover, we show that the completion of any triangulated category with respect to an internal aisle metric is a thick subcategory of the triangulated category itself.

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Charley Cummings, Sira Gratz. 2024-09-23. Metric completions of discrete cluster categories. https://arxiv.org/abs/2407.17369

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