3 Citations
Goodness in $n$-angulated categories
- Mathematics
- 2022
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
- Mathematics
- 2022
. 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
- Mathematics
- 2022
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
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…
Higher Toda brackets and the Adams spectral sequence in triangulated categories
- Mathematics
- 2015
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
- Mathematics
- 2001
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…
Homotopy cartesian diagrams in $n$-angulated categories
- MathematicsHomology, Homotopy and Applications
- 2019
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
- Mathematics
- 1996
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…