doi:10.1016/j.jfa.2024.110739engBosa, JoanVilalta, EduardPure *-homomorphismsART-2024-141400We introduce and study the notion of pureness for *-homomorphisms and, more generally, for cpc order-zero maps. After providing various important examples of pureness, we show our main result: Any composition of two pure maps factors through a pure object up to Cuntz equivalence. This is used to obtain several factorization results at the level of C⁎-algebras.2024http://zaguan.unizar.es/record/14782910.1016/j.jfa.2024.110739http://zaguan.unizar.es/record/147829oai:zaguan.unizar.es:147829info:eu-repo/grantAgreement/ES/DGA/E22-23Rinfo:eu-repo/grantAgreement/ES/MCINN/PID2020-113047GBJOURNAL OF FUNCTIONAL ANALYSIS 288, 3 (2024), 110739 [27 pp.]by-nchttps://creativecommons.org/licenses/by-nc/4.0/deed.esinfo:eu-repo/semantics/openAccess