On the Karoubi filtration of a category
There is a notion, due to Karoubi, of an additive category \({\mathcal U}\) being filtered by a full subcategory \({\mathcal A}\); it is the categorical analogue of an ideal \({\mathcal A}\) in a ring \({\mathcal U}\). When \({\mathcal U}\) and \({\mathcal A}\) are such categories, there are fibrations of spectra giving \(K\)-theory exact sequences associated to the sequence \({\mathcal A}\to{\mathcal U}\to{\mathcal U}/{\mathcal A}\); these fibrations have been used to prove excision results. In this paper the authors give new proofs for the fibrations based on Waldhausen's \(S\)-construction and generic fibration lemma.
scientific article; zbMATH DE number 1062414