CrossRef Open Access 2021

On (co)products of partial combinatory algebras, with an application to pushouts of realizability toposes

Jetze Zoethout

Abstrak

AbstractWe consider two preorder-enriched categories of ordered partial combinatory algebras: OPCA, where the arrows are functional (i.e., projective) morphisms, and OPCA†, where the arrows are applicative morphisms. We show that OPCA has small products and finite biproducts, and that OPCA† has finite coproducts, all in a suitable 2-categorical sense. On the other hand, OPCA† lacks all nontrivial binary products. We deduce from this that the pushout, over Set, of two nontrivial realizability toposes is never a realizability topos. In contrast, we show that nontrivial subtoposes of realizability toposes are closed under pushouts over Set.

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Jetze Zoethout

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Zoethout, J. (2021). On (co)products of partial combinatory algebras, with an application to pushouts of realizability toposes. https://doi.org/10.1017/s096012952100013x

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Informasi Jurnal

Tahun Terbit: 2021
Bahasa: en
Sumber Database: CrossRef
DOI: 10.1017/s096012952100013x
Akses: Open Access ✓