The existence of UFO implies projectively universal morphisms

0573345 - MÚ 2024 RIV US eng J - Článek v odborném periodiku
Balcerzak, M. - Kania, Tomasz
The existence of UFO implies projectively universal morphisms.
Proceedings of the American Mathematical Society. Roč. 151, č. 9 (2023), s. 3737-3742. ISSN 0002-9939. E-ISSN 1088-6826
Institucionální podpora: RVO:67985840
Klíčová slova: universal free object * UFO * projective universality * concrete category
Obor OECD: Pure mathematics
Impakt faktor: 1, rok: 2022
Způsob publikování: Omezený přístup
https://doi.org/10.1090/proc/16422

Let C be a concrete category. We prove that if C admits a universally free object F, then there is a projectively universal morphism u: F -> F, i.e., a morphism u such that for any B is an element of C and tau is an element of Mor(B) there exists an epimorphism pi is an element of Mor(F, B) such that pi tau = u pi. This builds upon and extends various ideas by Darji and Matheron [Proc. Amer. Math. Soc. 145 (2017), pp. 251-265] who proved such a result for the category of separable Banach spaces with contractive operators as well as certain classes of dynamical systems on compact metric spaces. Specialising from our abstract setting, we conclude that the result applies to various categories of Banach spaces/lattices/algebras, C*-algebras, etc.
Trvalý link: https://hdl.handle.net/11104/0343808