Peter Jorgensen
Triangulated categories of extensions and the Second Isomorphism Theorem for triangulated categories.
Fri, 01/13/2012 - 15:01 — SomNambulAuthors: Kiriko Kato, Peter Jorgensen
Subjects: Representation Theory
AbstractLet T be a triangulated category with triangulated subcategories X and Y. We
show that the subcategory of extensions X * Y is triangulated if and only if Y
* X is contained in X * Y.In this situation, we show the following analogue of the Second Isomorphism
Theorem: (X * Y) / X is equivalent to Y / (X \cap Y) and (X * Y) / Y is
equivalent to X / (X \cap Y).Symmetric Auslander and Bass categories.
Tue, 01/19/2010 - 16:01 — SomNambulAuthors: Kiriko Kato, Peter Jorgensen
Subjects: Commutative Algebra
AbstractWe define the symmetric Auslander category A^s(R) to consist of complexes of
projective modules whose left- and right-tails are equal to the left- and right
tails of totally acyclic complexes of projective modules.The symmetric Auslander category contains A(R), the ordinary Auslander
category. It is well known that A(R) is intimately related to Gorenstein
projective modules, and our main result is that A^s(R) is similarly related to
what can reasonably be called Gorenstein projective homomorphisms. Namely,
there is an equivalence of triangulated categories:
User login
