Lifting of recollements and gluing of partial silting sets

This paper focuses on recollements and silting theory in triangulated categories. It consists of two main parts. In the first part a criterion for recollement subcategories to lift torsion torsion-free triple (TTF triple) ambient categories with coproducts is proved. As consequence, lifting TTF triples possible stable repetitive algebras or self-injective finite length bounded derived separated Noetherian schemes. When, addition, outer are small linear conditions from sufficient up equivalence. second we use these results study problem constructing sets central category generating t-structure glued t-structures case Artin provide an explicit construction gluing classical objects.