… 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 …

… 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. …

… We revisit the abelian quotient category of conflations by … a unique exact substructure such
that it is a cluster quotient. … this abelian quotient is available in any triangulated category with …

… this correspondence is actually restriction of triangle functors between triangulated quotient
categories of the corresponding module categories. We review this theory and show how we …

… took the additive quotient. We obtain this way triangulated quotient categories and we show
the … In Section 4 we revisit tensor triangulated categories and study their behaviour within our …