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
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“A structure becomes architectural, and not sculptural, when its elements no longer have their justification in nature.”
—Guillaume Apollinaire (1880–1918)