论文标题
不明飞行物的存在暗示着普遍的态度意味着
The existence of UFO implies projectively universal morphisms
论文作者
论文摘要
令$ \ Mathcal C $为具体类别。我们证明，如果$ \ nathcal {c} $承认一个普遍免费的对象$ \ mathsf f $，那么有一种普遍的普遍态度$ \ u \ colon \ colon \ mathsf f \ to \ mathsf f $，即形态学$ $ $存在于{\ rm mor}（\ mathsf f，b）$中的表达$π\，使得$πτ=uπ$。这是基于Darji和Matheron（Proc。Am。Math。Soc。145（2017））的各种想法的基础，并证明了与承包商的可分离Banach空间以及紧凑型公制空间上的某些类型的动态系统的结果。我们从抽象的环境中进行专门研究，得出的结论是，结果适用于各种类别的Banach空间/格子/代数，C*-ergebras等。
Let $\mathcal C$ be a concrete category. We prove that if $\mathcal{C}$ admits a universally free object $\mathsf F$, then there is a projectively universal morphism $u\colon \mathsf F\to \mathsf F$, i.e., a morphism $u$ such that for any $B\in \mathcal{C}$ and $τ\in {\rm Mor}(B)$ there exists an epimorphism $π\in {\rm Mor}(\mathsf F, B)$ such that $πτ= u π$. This builds upon and extends various ideas by Darji and Matheron (Proc. Am. Math. Soc. 145 (2017)) 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.
