The existence of UFO implies projectively universal morphisms

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00573345" target="_blank" >RIV/67985840:_____/23:00573345 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1090/proc/16422" target="_blank" >https://doi.org/10.1090/proc/16422</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/proc/16422" target="_blank" >10.1090/proc/16422</a>

Result language
angličtina
Original language name
The existence of UFO implies projectively universal morphisms
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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