Stable Module Category - Triangulated Structure

Triangulated Structure

An exact sequence

in the usual module category defines an element of, and hence an element of, so that we get a sequence

Taking to be the translation functor and such sequences as above to be exact triangles, the stable module category becomes a triangulated category.

Read more about this topic:  Stable Module Category

Famous quotes containing the word structure:

    “Vashtar: So it’s finished. A structure to house one man and the greatest treasure of all time.
    Senta: And a structure that will last for all time.
    Vashtar: Only history will tell that.
    Senta: Sire, will he not be remembered?
    Vashtar: Yes, he’ll be remembered. The pyramid’ll keep his memory alive. In that he built better than he knew.”
    —William Faulkner (1897–1962)