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Universal coefficient theorem in triangulated categories

Teimuraz Pirashvili·Maria Julia Redondo
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Abstract

Let T be a triangulated category, A a graded abelian category and h: T -> A a homology theory on T with values in A. If the functor h reflects isomorphisms, is full and is such that for any object x in A there is an object X in T with an isomorphism between h(X) and x, we prove that A is a hereditary abelian category and the ideal Ker(h) is a square zero ideal which as a bifunctor on T is isomorphic to Ext^1_A(h(-)[1], h(-)).

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Teimuraz Pirashvili, Maria Julia Redondo. 2006-09-04. Universal coefficient theorem in triangulated categories. https://arxiv.org/abs/math/0604412

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