arXiv:math/0601185v5 [math.KT] 19 Jun 2006 Page 1 arXiv:math/0601185v5 [math.KT] 19 Jun
2006 ON DIFFERENTIAL GRADED CATEGORIES BERNHARD KELLER Abstract. Differential …

The central aim of this book is to understand modules and the categories they form through
associated structures and dimensions, which reflect the complexity of these, and similar …

This paper continues the development of the deformation theory of abelian categories
introduced in a previous paper by the authors. We show first that the deformation theory of …

In this paper we develop the basic infinitesimal deformation theory of abelian categories.
This theory yields a natural generalization of the well-known deformation theory of algebras …

We define model category structures on the category of chain complexes over a
Grothendieck abelian category depending on the choice of a generating family, and we …

We study when the heart of at-structure in a triangulated category D with coproducts is AB5
or a Grothendieck category. If D satisfies Brown representability, at-structure has an AB5 …

We study abelian envelopes for pseudo-tensor categories with the property that every object
in the envelope is a quotient of an object in the pseudo-tensor category. We establish an …

The Popescu–Gabriel theorem states that each Grothendieck abelian category is a
localization of a module category. In this paper, we prove an analogue where Grothendieck …

We define a tensor product of linear sites of which we investigate the functoriality properties.
Consequently, we define a tensor product of Grothendieck categories based upon their …

It is a result of Gabriel that hereditary torsion pairs in categories of modules are in bijection
with certain filters of ideals of the base ring, called Gabriel filters or Gabriel topologies. A …