The aim of this paper is to study silting-discrete triangulated categories. We establish a simple criterion for silting-discreteness in terms of 2-term silting objects. This gives a powerful tool to prove silting-discreteness of finite dimensional algebras. Moreover, we will show Bongartz-type Lemma for silting-discrete triangulated categories.

Triangulated categories were introduced in the mid 1960’s by J.L. Verdier in his thesis, reprinted in [15]. Axioms similar to Verdier’s were independently also suggested in [2]. Having their origins in algebraic geometry and algebraic topology, triangulated categories have by now become indispensable in many different areas of mathematics. Although the axioms might seem a bit opaque at first si...

We investigate certain categorical aspects of Voevodsky's triangulated categories motives. For this, various recollements for Grothendieck enriched functors and their derived are established. In order to extend these further with respect Serre's localization, the concept (strict) Voevodsky property Serre localizing subcategories is introduced. This inspired by celebrated theorem on homotopy inv...