arXiv:2609.22551 · v2

The category of nominal sets is locally monoidal closed

首次提交 2026-09-19 04:08

版本更新 2026-11-03 00:56

雷达观测 2026-11-04 23:41

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.