Topos物理理论基金会：IV。系统类别
A Topos Foundation for Theories of Physics: IV. Categories of Systems
摘要：
本文是系列文章中的第四篇，其目标是开发一种构建物理学理论的全新方法。其动机来自于解决引力量子理论中出现的某些深层问题的愿望。我们的基本论点是，构建一个物理学理论等价于在一个附着于该系统的某种形式语言的主题中找到一个表示。当topos是集合的范畴时，经典物理学就产生了。其他类型的理论采用不同的主题。本系列的前几篇文章是关于在一个系统中实现这个程序的。在本文中，我们转向考虑一组系统：特别是，我们感兴趣的复合系统的拓扑表示之间的关系，其成分的表示。我们还研究了两个系统的不交和的问题。我们处理这些问题的方法是构造一个系统的范畴，并找到整个范畴的拓扑表示。
英文摘要：
This paper is the fourth in a series whose goal is to develop a fundamentally new way of building theories of physics. The motivation comes from a desire to address certain deep issues that arise in the quantum theory of gravity. Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a certain formal language that is attached to the system. Classical physics arises when the topos is the category of sets. Other types of theory employ a different topos. The previous papers in this series are concerned with implementing this programme for a single system. In the present paper, we turn to considering a collection of systems: in particular, we are interested in the relation between the topos representation for a composite system, and the representations for its constituents. We also study this problem for the disjoint sum of two systems. Our approach to these matters is to construct a category of systems and to find a topos representation of the entire category.
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