# Heller triangulated categories

@article{Kuenzer2005HellerTC, title={Heller triangulated categories}, author={Matthias Kuenzer}, journal={Homology, Homotopy and Applications}, year={2005}, volume={9}, pages={233-320} }

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 E. Shifting a complex by 3 positions yields an outer shift functor on this category. Passing to the quotient modulo split acyclic complexes, Heller remarked that inner and outer shift become isomorphic, via an isomorphism satisfying still a further compatibility. Moreover, Heller remarked that a…

## 21 Citations

On lifting stable diagrams in Frobenius categories

- Mathematics
- 2005

Suppose given a Frobenius category E, i.e. an exact category with a big enough subcategoryB of bijectives. LetE :=E=B denote its classical stable category. For example, we may take E to be the…

On adjoint functors of the Heller operator

- Mathematics
- 2011

Given an abelian category A with enough projectives, we can form its stable category _A_ := A/Proj(A)$. The Heller operator Omega : _A_ -> _A_ is characterised on an object X by a choice of a short…

Comparison of spectral sequences involving bifunctors

- Mathematics
- 2009

Suppose given functorsA A 0 F B G C between abelian categories, an object X in A and an object X 0 inA 0 such that F (X; ), F ( ;X 0 ) and G are left exact, and such that further conditions hold. We…

Separable extensions in tt-geometry and generalized Quillen stratification

- Mathematics
- 2013

We study the continuous map induced on spectra by a separable extension of tensor-triangulated categories. We determine the image of this map and relate the cardinality of its fibers to the degree of…

Separable extensions in tensor-triangular geometry and generalized Quillen stratification

- Mathematics
- 2013

We study the continuous map induced on spectra by a separable extension of tensor-triangulated categories. We determine the image of this map and relate the cardinality of its fibers to the degree of…

Comparison of spectral sequences involving bifunctors

- Mathematics
- 2006

Suppose given functors A x A' -F-> B -G-> C between abelian categories, an object X in A and an object X' in A' such that certain conditions hold. We show that, E_1-terms exempt, the Grothendieck…

A Sufficient Criterion for Homotopy Cartesianess

- MathematicsAppl. Categorical Struct.
- 2011

A commutative quadrangle in a Verdier triangulated category such that there exists an induced isomorphism on the horizontally taken cones is homotopy cartesian if and only if the endomorphism ring of the initial or the terminal corner object of this quadrangles satisfies a finiteness condition.

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