Suppose given a Frobenius category E, ie an exact category with a big enough subcategory
B of bijectives. Let E:= E/B denote its classical homotopy category. For example, we may …

It is shown that the idempotent completion of the additive hull of the tensor product of the
residue category of the category of paths of a locally finite quiver modulo an admissible ideal …

We show that, over an arbitrary commutative ring, the localizations of the categories of dg
categories, of unital and of strictly unital $ A_\infty $ categories with respect to the …

An additive functor F: A → B between additive categories is said to be objective, provided
any morphism f in A with F (f)= 0 factors through an object K with F (K)= 0. We concentrate on …

This thesis explores the relation between module categories over small differential graded
(abbreviated DG) categories on the one hand, and well generated triangulated categories …

This article provides some basic results on weight structures, weight complex functors and
homotopy categories. We prove that the full subcategories K (A)^{w< n}, K (A)^{w> n}, K (A) …

Let $\mathscr {A} $ be an extension closed proper abelian subcategory of a triangulated
category $\mathscr {T} $, with no negative 1 and 2 extensions. From this, two functors from …

We show that, over an arbitrary commutative ring, the localizations of the categories of dg
categories, of unital and of strictly unital A∞ categories with respect to the corresponding …

We study rank functions on a triangulated category 𝒞 via its abelianisation mod⁡ C. We
prove that every rank function on 𝒞 can be interpreted as an additive function on mod⁡ C …

Let X be a semibrick in an extriangulated category C. Let T be the filtration subcategory
generated by X. We give a one-to-one correspondence between simple semibricks and …