… The K-theory of τ-tilting theory is discussed in the fourth part … invariant encodes much of its
τ-tilting theory. We warn the reader … since the introduction of τ-tilting theory, to our knowledge, …

… We introduce a relative tilting theory in abelian categories and show that this work offers a
… new tilting theories in categories that can be embedded nicely in an abelian category. In …

… of extriangulated categories … theory in extriangulated categories and τ-tilting theory. In this
article, let k be a field and B be a Hom-finite, Krull-Schmidt, k-linear extriangulated category …

… Perpendicular categories On the other hand we consider the theory of perpendicular cate…
in 1991 which focuses on the study of perpendicular categories for path algebras. One of the …

… In this article, we discuss an abelian version of τ-tilting theory. … Let A be an abelian category
with enough projectives. Then … A be a Hom-finite abelian category over k. We assume that A …

… in studying τ-tilting theory in arbitrary abelian categories with … τ in such general categories,
the definition of support τ-tilting … We follow [29,31] to define support τ-tilting subcategories. …

… bijection between support τ-tilting subcategories and certain τ-cotorsion pairs. Given a support
τ-tilting subcategory T , we find a subcategory E T of E which is an exact category and T is …

… Finally, we say that T is support τ-tilting if it is a τ-tilting … We suppose now that A is τ-tilting
finite. An important ingredient for … Let A be a finite-dimensional algebra that is τtilting finite. The …

… The notion of torsion classes in an abelian category was introduced by Dickson [13] to
generalize the notion of torsion abelian groups. They are subcategories closed under taking …

… The paper is organized as follows: After recall some definitions and basic properties
related to τ-tilting theory in Section 2, we introduce the definition of c-vectors for finite-dimensional …