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arXiv · 1201.2499

Triangulated subcategories of extensions, stable t-structures, and triangles of recollements

Peter Jorgensen·Kiriko Kato
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Abstract

In a triangulated category T with a pair of triangulated subcategories X and Y, one may consider the subcategory of extensions X*Y. We give conditions for X*Y to be triangulated and use them to provide tools for constructing stable t-structures. In particular, we show how to construct so-called triangles of recollements, that is, triples of stable t-structures of the form (X,Y), (Y,Z), (Z,X). We easily recover some triangles of recollements known from the literature.

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Peter Jorgensen, Kiriko Kato. 2015-05-06. Triangulated subcategories of extensions, stable t-structures, and triangles of recollements. https://arxiv.org/abs/1201.2499

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