Bijective correspondences are established between (1) silting objects,(2) simple-minded
collections,(3) bounded t-structures with length heart and (4) bounded co-t-structures. These …

We introduce the new concept of silting modules. These modules generalize tilting modules
over an arbitrary ring, as well as support-tilting modules over a finite dimensional algebra …

We study two kinds of reduction processes of triangulated categories, that is, silting
reduction and Calabi–Yau reduction. It is shown that the silting reduction $\mathcal …

The exchange graph of a cluster algebra encodes the combinatorics of mutations of clusters.
Through the recent" categorifications" of cluster algebras using representation theory one …

We show that Quillenʼs small object argument works for exact categories under very mild
conditions. This has immediate applications to cotorsion pairs and their relation to the …

In this article, we initiate the study of hereditary extriangulated categories. Many important
categories arising in representation theory in connection with various theories of mutation …

Recollements of derived module categories are investigated, using a new technique,
ladders of recollements, which are maximal mutation sequences. The position in the ladder …

Abstract If (A, B) and (A′, B′) are co-t-structures of a triangulated category, then (A′, B′)
is called intermediate if A⊆ A′⊆ Σ A. Our main results show that intermediate co-t …

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 silting and …

We introduce the notion of noncompact (partial) silting and (partial) tilting sets and objects in
any triangulated category D with arbitrary (set-indexed) coproducts. We show that …