We define a dimension for a triangulated category. We prove a representability Theorem for
a class of functors on finite dimensional triangulated categories. We study the dimension of …

The paper contains general results on the uniqueness of a DG enhancement for triangulated
categories. As a consequence we obtain such uniqueness for the unbounded derived …

We associate a $ t $-structure to a family of objects in $\boldsymbol {\mathsf {D}}(\mathcal
{A}) $, the derived category of a Grothendieck category $\mathcal {A} $. Using general …

We provide an example of two closed model categories having equivalent homotopy
categories but different Waldhausen K-theories. We also show that there cannot exist a …

We study (not necessarily connected) Z-graded A-infinity-algebras and their A-infinity-
modules. Using the cobar and the bar construction and Quillen's homotopical algebra, we …

We define the spectrum of a tensor triangulated category as the set of so-called prime ideals,
endowed with a suitable topology. In this very generality, the spectrum is the universal space …

We show that the idempotent completion of a triangulated category has a natural structure of
a triangulated category. The idempotent completion of the bounded derived category of an …

Extriangulated categories were introduced by Nakaoka and Palu by extracting the
similarities between exact categories and triangulated categories. A notion of mutation of …

The notion of quotient and localization of abelian categories by dense subcategories (ie,
Serre classes) was introduced by Gabriel, and plays an important role in ring theory [6, 131 …

arXiv:0804.1163v2 [math.AG] 16 Apr 2008 Page 1 arXiv:0804.1163v2 [math.AG] 16 Apr
2008 REMARKS ON GENERATORS AND DIMENSIONS OF TRIANGULATED …