The category of nominal sets is locally monoidal closed

2026-09-18

AI Summary

本文解决了名义集范畴的局部闭性质问题，通过展示每个单子结构如何在所有切片范畴上诱导出单子结构。

Abstract

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.

Problem

• nominal sets
• monoidal closed
• slice categories
• separated product

Innovation

• monoidal closed structure
• slice categories
• separated product
• nominal sets