## 79 Citations

Torsion theories and Auslander-Reiten sequences

- Mathematics
- 2011

Chapter 0 gives a gentle background to the thesis. It begins with some general notions and concepts from homological algebra. For example, not only are the notions of universal property and of…

Homotopical algebra and triangulated categories

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 1995

Abstract We study here the connections between the well known Puppe-Verdier notion of triangulated category and an abstract setting for homotopical algebra, based on homotopy kernels and cokernels,…

The axioms for n–angulated categories

- Mathematics
- 2011

We discuss the axioms for an n-angulated category, recently introduced by Geiss, Keller and Op- permann in (2). In particular, we introduce a higher "octahedral axiom", and show that it is equivalent…

Generalised Moore spectra in a triangulated category

- Mathematics
- 2009

In this paper we consider a construction in an arbitrary triangulated category $${\fancyscript {T}}$$ which resembles the notion of a Moore spectrum in algebraic topology. Namely, given a compact…

Triangulated functors, homological functors, tilts, and lifts

- Mathematics
- 2003

Abstract. Let T be a triangulated category and let X be an object of T. This paper studies the questions: Does there exist a triangulated functor G : D(ℤ) T with G(ℤ)≌X? Does there exist a…

Heller triangulated categories

- Mathematics
- 2005

Let E be a Frobenius category. Let E denote its stable category. The shift functor on E induces, by pointwise application, an inner shift functor on the category of acyclic complexes with entries in…

Prime tensor ideals in some triangulated categories of C*-algebras

- Mathematics
- 2008

iii Abstract The purpose of this thesis is to inaugurate the application of algebraico-geometric ideas, in the form of Paul Balmer’s tensor triangular geometry [Bal05], to the study of such tensor…

The Fundamental Group of a Morphism in a Triangulated Category

- Mathematics
- 2013

We introduce the fundamental group of a morphism in a triangulated category and show that the groupoid of distinguished triangles containing a given extension of objects from an abelian category is…

2 8 Fe b 20 07 Heller triangulated categories

- Mathematics
- 2009

Let E be a Frobenius category. Let E denote its stable category. The shift functor on E induces, by pointwise application, an inner shift functor on the category of acyclic complexes with entries in…

## References

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