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

Peter Jorgensen, Kiriko Kato

• 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.