… Here we shall introduce a notion of partial silting object in any triangulated category with …
In fact any such partial silting object defines a t-structure in the triangulated category whose …

… silting subcategories/objects of triangulated categories and … –Yau triangulated categories
containing a silting subcategory and l … remark, where we say that a category is skeletally small if …

… We give an overview of recent developments in silting theory. After an introduction on
torsion pairs in triangulated categories, we discuss and compare different notions of …

… investigate silting-discreteness for a particularly important class of triangulated categories. …
give a characterisation of silting-discreteness for C using cluster-tilting theory for the cluster …

… of triangulated categories, that is, silting reduction and Calabi-Yau reduction. It is shown that
the silting reduction T /thickP of a triangulated category … as a certain subfactor category of T , …

… the relative singularity category T ω for a triangulated category T with … silting theory in
triangulated categories [28]. This generalizes the above-mentioned variants of singularity categories…

… triangulated categories, we show that the heart of a (co)silting t-structure is a Grothendieck
category … If we further assume our triangulated category to be algebraic, it follows that the …

… Nowadays, silting theory and silting reduction play important roles in the research of
triangulated categories, especially derived categories. In [KY], it is shown that silting objects have …

… D b ( Λ ) and D b ( H ) are equivalent as triangulated categories. The … of a triangulated category
with respect to a silting object, … Any triangulated category C in this article is assumed to be …

… triangulated category is silting-connected. There are three levels of silting-connectedness:(i)
silting-connected (ii) strongly silting… that a given triangulated category is silting-discrete [AAC…