名义集合范畴是局部幺半群闭的
The category of nominal sets is locally monoidal closed
- Dalhousie University（达尔豪斯大学）
- University of South Carolina（南卡罗来纳大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文证明名义集合范畴Nom上的每个幺半群闭结构都能诱导所有切片范畴上的相应结构，从而Nom是局部分离闭的。
AI中文摘要：
由Pitts和Gabbay提出的名义集合范畴Nom，被用作带有变量绑定的抽象语法语义的框架。众所周知，Nom是一个拓扑斯，也称为Schanuel拓扑斯，特别地，由此可知Nom是局部闭的，即每个切片范畴Nom/X都是笛卡尔闭的。在本文中，我们证明Nom具有一个更强的性质：Nom上的每个幺半群（闭）结构都会诱导所有切片范畴Nom/X上的幺半群（闭）结构。Nom上一个特别值得关注的幺半群闭结构是分离积A * B，其右伴随A -* B被称为分离函数空间。特别地，由此可知Nom是局部分离闭的。
英文摘要：
The category Nom of nominal sets was proposed by Pitts and Gabbay as a setting for the semantics of abstract syntax with variable bindings. It is well-known that Nom is a topos, also known as the Schanuel topos, and in particular it follows that Nom is locally closed, i.e., every slice category Nom/X is cartesian-closed. In this paper, we show that Nom has a much stronger property: every monoidal (closed) structure on Nom induces a monoidal (closed) structure on all slice categories Nom/X. One monoidal closed structure of particular interest on Nom is the separated product A * B, whose right adjoint A -* B is called the separated function space. In particular, it follows that Nom is locally separatedly closed.
