caa a22 4500 445378832 CHVBK 20180317143011.0 cr unu---uuuuu 170323e20110601xx s 000 0 eng 10.1007/s10485-009-9198-z doi (NATIONALLICENCE)springer-10.1007/s10485-009-9198-z Lifting and Restricting Recollement Data [Elektronische Daten] [Pedro Nicolás, Manuel Saorín] We study the problem of lifting and restricting TTF triples (equivalently, recollement data) for a certain wide type of triangulated categories. This, together with the parametrizations of TTF triples given in Nicolás and Saorín (Parametrizing recollement data for triangulated categories. To appear in J. Algebra), allows us to show that many well-known recollements of right bounded derived categories of algebras are restrictions of recollements in the unbounded level, and leads to criteria to detect recollements of general right bounded derived categories. In particular, we give in Theorem 1 necessary and sufficient conditions for a right bounded derived category of a differential graded (=dg) category to be a recollement of right bounded derived categories of dg categories. Theorem 2 considers the case of dg categories with cohomology concentrated in non-negative degrees. In Theorem 3 we consider the particular case in which those dg categories are just ordinary algebras. Springer Science+Business Media B.V., 2009 Derived category nationallicence DG category nationallicence Morita theory nationallicence Recollement nationallicence Triangulated category nationallicence Nicolás Pedro Departamento de Matemáticas, Universidad de Murcia, Aptdo. 4021, Espinardo, 30100, Murcia, Spain aut Saorín Manuel Departamento de Matemáticas, Universidad de Murcia, Aptdo. 4021, Espinardo, 30100, Murcia, Spain aut Applied Categorical Structures Springer Netherlands 19/3(2011-06-01), 557-596 0927-2852 19:3<557 2011 19 10485 https://doi.org/10.1007/s10485-009-9198-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10485-009-9198-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Nicolás Pedro Departamento de Matemáticas, Universidad de Murcia, Aptdo. 4021, Espinardo, 30100, Murcia, Spain aut NATIONALLICENCE 700 1- Saorín Manuel Departamento de Matemáticas, Universidad de Murcia, Aptdo. 4021, Espinardo, 30100, Murcia, Spain aut NATIONALLICENCE 773 0- Applied Categorical Structures Springer Netherlands 19/3(2011-06-01), 557-596 0927-2852 19:3<557 2011 19 10485 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer