An algebra is said to be-tilting finite provided it has only a finite number of-rigid objects up to
isomorphism. To each such algebra, we associate a category whose objects are the wide …

REPORT ON THE FINITENESS OF SILTING OBJECTS Page 1 Proceedings of the Edinburgh
Mathematical Society (2021) 64, 217–233 doi:10.1017/S0013091521000109 REPORT ON THE …

The class of support-tilting modules was introduced to provide a completion of the class of
tilting modules from the point of view of mutations. In this article, we study-tilting finite …

We prove that a finite dimensional algebra is τ-tilting finite if and only if it does not admit
large silting modules. Moreover, we show that for a τ-tilting finite algebra A there is a …

This note compares τ-tilting modules and maximal rigid objects in the context of 2-Calabi-
Yau triangulated categories. Let 𝓒 be a 2-Calabi-Yau triangulated category with suspension …

Abstract Let E=(A, S) be an exact category with enough projectives P. We introduce the
notion of support τ-tilting subcategories of E. It is compatible with the existing definitions of …

The class of support-tilting modules was introduced recently by Adachi et al. These modules
complete the class of tilting modules from the point of view of mutations. Given a finite …

For classes of algebras defined in nonhomological terms it is often of interest to look for a
homological description. For example the Auslander algebras, that is the algebras which are …

Happel [6] and Cline, Parshall and Scott [4] showed that the tilting functors of Happel and
Ringel [8] can be interpreted in terms of an equivalence of derived categories of the module …

Let k be a fixed algebraically closed field. For a finite-dimensional k-algebra A, we shall
denote by modA the category of finite-dimensional right A-modules, and by Db (A) the …