2009/02/23 by Gonçalo Tabuada, Tabuada, Goncalo
Mathematics · #18D20 #19D55 #55P43 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)
paper · pdf · doi:10.48550/arxiv.0902.3888
openalex publication_date 2009/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we pursue the study of spectral categories initiated in [26]. More precisely, we construct the Universal matrix invariant of spectral categories, i.e. a functor U with values in an additive category Add, which inverts the Morita equivalences, satisfies matrix invariance, and is universal with respect to these two properties. For example, the algebraic K-theory and the topological Hochschild and cyclic homologies are matrix invariants, and so they factor uniquely throw U. As an application, we obtain for free non-trivial trace maps from the Grothendieck group to the topological Hochschild homology ones.