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