2013/01/21 by Clark Barwick, Barwick, C.
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)
paper · pdf · doi:10.48550/arxiv.1301.4725
openalex publication_date 2013/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that the K-theory of an exact quasicategory can be computed via a higher categorical variant of the Q construction. This construction yields a quasicategory whose weak homotopy type is a delooping of the K-theory space. We show that the direct sum endows this homotopy type with the structure of a infinite loop space, which agrees with the canonical one. Finally, we prove a proto-devissage result, which gives a necessary and sufficient condition for a "nilimmersion" of stable quasicategories to be a K-theory equivalence. In particular, we prove that a well-known conjecture of Ausoni and Rognes is equivalent to the weak contractibility of a particular quasicategory.