2024/07/13 by Herbera, Dolors, Pitsch, Wolfgang, Saorín, Manuel +1
#18G10 #FOS: Mathematics #K-Theory and Homology (math.KT) #Primary 18G25 #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Secondary 18E10
paper · doi:10.48550/arxiv.2407.09741
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.