范畴子系统独立性作为态射余可能性
Categorial subsystem independence as morphism co-possibility
摘要：
本文提出了一般范畴（不一定是具体范畴）中对象的子范畴独立性的概念。子对象独立性是代数相对论量子场论中所谓子系统独立性的范畴推广。本文所表述的子对象独立性的内容是态射余可能性：如果一个对象的两个子对象上的任何两个态射都可以由较大对象上的一个态射共同实现，则该对象的两个子对象将被定义为独立的。本文研究了子对象独立性的一般特征，提出了C* 代数范畴中的子对象关于C*-代数上的完全正单位保持线性映射作为态射的子对象独立性作为自然的子系统独立性公理，用以表达量子场论范畴方法中协变函子的相对论局部性.
英文摘要：
This paper formulates a notion of independence of subobjects of an object in a general (i.e. not necessarily concrete) category. Subobject independence is the categorial generalization of what is known as subsystem independence in the context of algebraic relativistic quantum field theory. The content of subobject independence formulated in this paper is morphism co-possibility: two subobjects of an object will be defined to be independent if any two morphisms on the two subobjects of an object are jointly implementable by a single morphism on the larger object. The paper investigates features of subobject independence in general, and subobject independence in the category of C* algebras with respect to operations (completely positive unit preserving linear maps on C*-algebras) as morphisms is suggested as a natural subsystem independence axiom to express relativistic locality of the covariant functor in the categorial approach to quantum field theory.
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