关于“外延PER”的注记
A Note on "Extensional PERs"
摘要：
在P.Freyd、P.Mulry、G. Rosolini和D. Scott，引入了一个由“点完全可拓PER”和可计算映射构成的范畴$\mathcal{C}$，给出了一个相对于有限函子类的\emph{algebraically compact category}的实例.代数紧性是范畴上的一个综合条件，它保证了包含该范畴内函子的递归方程的解。我们扩展的结果，包括所有内部函子$\mathcal{C}$时，$\mathcal{C}$被视为一个完整的内部范畴的有效拓扑。这是使用两个一般性的结果：一个是关于一般的内部函子，另一个是关于有效拓扑中的内部函子。
英文摘要：
In the paper "Extensional PERs" by P. Freyd, P. Mulry, G. Rosolini and D. Scott, a category $\mathcal{C}$ of "pointed complete extensional PERs" and computable maps is introduced to provide an instance of an \emph{algebraically compact category} relative to a restricted class of functors. Algebraic compactness is a synthetic condition on a category which ensures solutions of recursive equations involving endofunctors of the category. We extend that result to include all internal functors on $\mathcal{C}$ when $\mathcal{C}$ is viewed as a full internal category of the effective topos. This is done using two general results: one about internal functors in general, and one about internal functors in the effective topos.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
