Triangulated subcategories of extensions, stable t-structures, and triangles of recollements
Representation Theory
2015-05-07 v4 Category Theory
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.
Keywords
Cite
@article{arxiv.1201.2499,
title = {Triangulated subcategories of extensions, stable t-structures, and triangles of recollements},
author = {Peter Jorgensen and Kiriko Kato},
journal= {arXiv preprint arXiv:1201.2499},
year = {2015}
}
Comments
12 pages. This is the final accepted version which will appear in the Journal of Pure and Applied Algebra