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A poisonous example to explicit resolutions of unbounded complexes

A poisonous example to explicit resolutions of unbounded complexes

We show that various methods for explicitly building resolutions of unbounded complexes in fact fail when applied to a rather simple and explicit complex. We show that one way to rescue these methods is to assume Roos (Ab.4$^*$)-$k$ axiom, which we adapt to encompass also resolutions in the framework of …