A poisonous example to explicit resolutions of unbounded complexes
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.
Fields of Study & Subjects
Computational Drug Discovery Methods
History and advancements in chemistry
Chemistry and Stereochemistry Studies
Publication details
- Journal / source
- Publicacions Matemàtiques
- Volume
- 70
- Pages
- 445–492
- Publication date
- 17 June 2026
- Language
- EN