论文标题
关于可实现性替补的求职者的存在
On the Existence of Pushouts of Realizability Toposes
论文作者
论文摘要
我们考虑了有序的PCAS的两个预订类别：$ \ Mathsf {opca} $，其中箭头是功能性形态，而$ \ Mathsf {pca} $，其中箭头是应用词法。我们表明$ \ mathsf {opca} $具有小型产品和有限的两种产品，并且$ \ mathsf {pca} $具有有限的coproducts，所有这些都具有合适的2类分类意义。另一方面，$ \ mathsf {pca} $缺少所有非平凡的二进制产品。我们从中推断出，两个非平地可实现的popers的求职者超过$ \ mathsf {set} $从来都不是可实现的topos。
We consider two preorder-enriched categories of ordered PCAs: $\mathsf{OPCA}$, where the arrows are functional morphisms, and $\mathsf{PCA}$, where the arrows are applicative morphisms. We show that $\mathsf{OPCA}$ has small products and finite biproducts, and that $\mathsf{PCA}$ has finite coproducts, all in a suitable 2-categorical sense. On the other hand, $\mathsf{PCA}$ lacks all nontrivial binary products. We deduce from this that the pushout, over $\mathsf{Set}$, of two nontrivial realizability toposes is never a realizability topos.
