On the Existence of Pushouts of Realizability Toposes
Jetze Zoethout

TL;DR
This paper investigates the categorical properties of ordered PCAs and shows that certain pushouts of realizability toposes over Set cannot be realizability toposes, revealing limitations in their categorical constructions.
Contribution
It establishes the existence of small products and finite biproducts in OPCA, finite coproducts in PCA, and proves the non-existence of certain pushouts of realizability toposes.
Findings
OPCA has small products and finite biproducts.
PCA has finite coproducts.
Pushouts of two nontrivial realizability toposes over Set are not realizability toposes.
Abstract
We consider two preorder-enriched categories of ordered PCAs: , where the arrows are functional morphisms, and , where the arrows are applicative morphisms. We show that has small products and finite biproducts, and that has finite coproducts, all in a suitable 2-categorical sense. On the other hand, lacks all nontrivial binary products. We deduce from this that the pushout, over , of two nontrivial realizability toposes is never a realizability topos.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsConstraint Satisfaction and Optimization
