Thursday, September 18, 15:15, 7.527

Simone Virili (Barcelona), A poisonous example to explicit resolutions of unbounded complexes.

Abstract:
We will show that various methods for explicitly building resolutions of unbounded complexes fail when applied to a rather simple and explicit complex. In fact, one way to rescue these methods is to assume Roos' (Ab.4*)-k axiom, which we adapt to encompass resolutions in the framework of relative homological algebra.
In the end we discuss the existence of model structures for relative homological algebra for unbounded complexes under the relative (Ab.4*)-k condition, and present a variety of examples where our results apply. In particular, we will show that, for any bicomplete Abelian category A with exact coproducts, there is an Abelian model structure on Ch(A) whenever A has an n-tilting object for some n in ℕ.
[This is a joint project with D.HERBERA, W.PITSCH, and M.SAORÍN]