A poisonous example to explicit resolutions of unbounded complexes
Year: 2026
Type: article
Abstract: 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 relative homological algebra. In the end we discuss the existence of model structures for relative homological algebra for unbounded complex under the relative (Ab.4$^*$)-$k$ condition, and present a variety of examples where our results apply.
Source: Publicacions Matemàtiques
Authors: Dolors Herbera, Wolfgang Pitsch, Manuel Saorín, Simone Virili
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4400702817