… D -mutation pair of subcategories in a triangulated category without assumption of Ext C 1 (
… triangulated category C , showed that the quotient category U / [ X ] is a triangulated category. …

… In Section 3 we study a quotient functor from a triangulated category to an abelian category
with projective … We revisit the last example presented in [11]. This is an example of an abelian …

… We show that a certain quotient category of s-def , the category of s-deflations … For both
triangulated categories and exact categories, cluster-tilting subcategories provide a way to …

… As usual we view S1 DR=Z as the quotient of its universal cover R by the fundamental
group Z; this identifies … Next let us revisit Theorem 6.6, the theorem identifying each of ŒT c …

… This paper studies the derived category of the Quot scheme of rank d locally free quotients
… for triangulated categories (see [Huy, Nee96, BvdB]). Let D be a triangulated category with …

… topology, triangulated categories have by now … quotient T /S of a triangulated category T
by a triangulated subcategory S is defined by a universal property with respect to triangulated …

… of a group G on a triangulated category T , the “quotient category” Tg , or the category of G-…
X correspond to coherent sheaves on the quotient variety X/G. On the categorical level, the …

… quotient of an extriangulated category such that the ideal is the kernel of a functor from this
extriangulated category to an abelian category… satisfied on triangulated and exact categories, …

… • take the Verdier quotient modulo the thick triangulated subcategory generated by: … In
Section 2.4, we revisit Ayoub’s proof and give some improvement of his theorems (see Theorem …

… categories generalize both triangulated and exact categories… subquotient categories of
extriangulated categories arising … , and give some applications in triangulated and exact cases. …