Arrow algebras

Fuente: arXiv
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Main Authors: Berg, Benno van den, Briet, Marcus
Format: Preprint
Published: 2023
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author Berg, Benno van den
Briet, Marcus
author_facet Berg, Benno van den
Briet, Marcus
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2308_14096
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Arrow algebras
Berg, Benno van den
Briet, Marcus
Category Theory
Logic
03B40, 03G30, 18B25, 18F70
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.
title Arrow algebras
topic Category Theory
Logic
03B40, 03G30, 18B25, 18F70
url https://arxiv.org/abs/2308.14096