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Results tagged with triangulated-categories
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user 98863
A triangulated category is an additive category equipped with the additional structure of an autoequivalence (called the translation functor) and a class of of triangles satisfying certain axioms.
4
votes
1
answer
321
views
Does localization at quasi-isomorphisms imply homotopy invariance?
Usually, the derived category of some abelian category $A$ (I'm happy already with $A$-mod) is defined first taking chain complexes up to homotopy, and then localize at quasi-isomorphisms.
My question …
- 1,028
3
votes
Accepted
Homotopy equivalences and Mapping Cones
It is true. It is not trivial (this is an opinion), however it is standard. In any triangulated category, two objects and a map determine the third, up to (usually non unique) isomorphism. And the cat …
- 1,028
4
votes
A toy example of a tensor triangulated category?
Take a finite dimensional Hopf algebra $H$, the category of $H$-modules is Frobenius (projectives=injectives and there is enough of both); e.g. take $H$ to be the group algebra of a finite group. So …
- 1,028