2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63278We define KK-theory spectra associated to C*-categories and look at certain instances of the Kasparov product at this level. This machinery is used to give a description of the analytic assembly map as a natural map of spectra.This is an updated version of an existing article. In this new version the machinery developed works in greater generality than the old versionK-Theory and Homology19K35; 55P42text