Non-connective K- and Nil-spectra of additive categorie

2013/03/06 by Wolfgang Lueck, Lueck, Wolfgang, Wolfgang Steimle +1 · 2 citations
Mathematics · #19D35 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.KT #msc:19D35

paper · pdf · doi:10.48550/arxiv.1303.1272

31 pages, to appear in the Proceedings of the Fourth Arolla Conference on Algebraic Topology 2012, Contemporary Mathematics, American Mathematical Society, Providence, RI

openalex publication_date 2013/03/06 · arxiv created 2013/09/04 · arxiv updated 2013/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present an elementary construction of the non-connective algebraic K-theory spectrum associated to an additive category following the contracted functor approach due to Bass. It comes with a universal property that easily allows us to identify it with other constructions, for instance with the one of Pedersen-Weibel in terms of Zⁱ-graded objects and bounded homomorphisms.

Citations

• Inheritance of Isomorphism Conjectures under colimits
• Modules of topological spaces, applications to homotopy limits andE ? structures
• K- and L-theory of group rings over GL_n(Z)

Cited by

• Survey on the Farrell-Jones Conjecture
• A twisted Bass-Heller-Swan decomposition for the algebraic K-theory of additive categories

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