Arrow algebras
Category Theory
2025-10-13 v5 Logic
Abstract
In this paper we introduce arrow algebras, simple algebraic structures which induce elementary toposes through the tripos-to-topos construction. This includes localic toposes as well as various realizability toposes, in particular, those realizability toposes which are obtained from partial combinatory algebras. Since there are many examples of arrow algebras and arrow algebras have a number of closure properties, including a notion of subalgebra given by a nucleus, arrow algebras provide a flexible tool for constructing toposes; we illustrate this by providing some general tools for creating toposes for Kreisel's modified realizability.
Cite
@article{arxiv.2308.14096,
title = {Arrow algebras},
author = {Benno van den Berg and Marcus Briet},
journal= {arXiv preprint arXiv:2308.14096},
year = {2025}
}
Comments
Revised version after comments by second referee