On good morphisms of exact triangles

@article{Christensen2020OnGM,
  title={On good morphisms of exact triangles},
  author={J. Daniel Christensen and Martin Frankland},
  journal={arXiv: Algebraic Topology},
  year={2020}
}
View PDF on arXiv
3 Citations
Background Citations
2

3 Citations

Goodness in $n$-angulated categories
We generalise the notions of good, middling good, and Verdier good morphisms of distinguished triangles in triangulated categories, first introduced by Neeman, to the setting of n -angulated…
Ideal mutations in triangulated categories and generalized Auslander-Reiten theory
. We introduce the notion of ideal mutations in a triangulated category, which generalizes the version of Iyama and Yoshino [15] by replacing approximations by objects of a subcategory with…
Homotopy cartesian squares in extriangulated categories
Let ( C , E , s ) be an extriangulated category. Given a composition of two commutative squares in C , if two commutative squares are homotopy cartesian, then their composition is also a homotopy…

References

SHOWING 1-10 OF 15 REFERENCES
Some new axioms for triangulated categories
Heller triangulated categories
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…
Higher Toda brackets and the Adams spectral sequence in triangulated categories
The Adams spectral sequence is available in any triangulated category equipped with a projective or injective class. Higher Toda brackets can also be defined in a triangulated category, as observed…
The Additivity of Traces in Triangulated Categories
Abstract We explain a fundamental additivity theorem for Euler characteristics and generalized trace maps in triangulated categories. The proof depends on a refined axiomatization of symmetric…
OBSTRUCTION THEORY IN MODEL CATEGORIES
Abstract representation theory of Dynkin quivers of type A
Homotopy cartesian diagrams in $n$-angulated categories
It has been proved by Bergh and Thaule that the higher mapping cone axiom is equivalent to the higher octahedral axiom for n-angulated categories. In this note, we use homotopy cartesian diagrams to…
Modules and Group Algebras
1 Augmentations, nilpotent ideals, and semisimplicity.- 2 Tensor products, Homs, and duality.- 3 Restriction and induction.- 4 Projective resolutions and cohomology.- 5 The stable category.- 6…
Representations and Cohomology
REPRESENTATIONS AND COHOMOLOGY I: Basic representation theory of finite groups and associative algebras
...
...