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arXiv · 2609.22551

The category of nominal sets is locally monoidal closed

Fahimeh Bayeh·Peng Fu·Peter Selinger
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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.

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Fahimeh Bayeh, Peng Fu, Peter Selinger. 2026-09-18. The category of nominal sets is locally monoidal closed. https://arxiv.org/abs/2609.22551

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