多项式多项式的固定点问题
Problems with fixpoints of polynomials of polynomials
AI总结：
本文研究了容器范畴中特定终.functors的固定点，探讨了初始代数、终端余代数及另一种固定点ζ的计算方法，并通过ζ表达式和容器解释捕捉了Weihrauch度量。
摘要：
受可计算分析应用启发，本文研究了容器范畴中特定终.functors的固定点。更具体地说，我们关注在纤维相反的余域纤维上方的纤维终.functors，这些终.functors本身可以表示为多项式终.functors的家族。在此设定下，我们展示了如何计算初始代数、终端余代数和另一种固定点ζ。然后，我们探索了受Weihrauch复杂度和通常自由多项式单子构造启发的若干衍生操作符。我们引入ζ表达式作为μ-双完备范畴的语法扩展，增加了ζ绑定器和并行积，从而在容器中自然地具有含义。通过在类型2可计算映射的范畴中解释某些ζ表达式，我们能够捕捉从{0,1}上的闭合选择到无限奇偶游戏确定性的Weihrauch度量，通过一个
英文摘要：
Motivated by applications in computable analysis, we study fixpoints of certain endofunctors over categories of containers. More specifically, we focus on fibred endofunctors over the fibrewise opposite of the codomain fibration that can be themselves be represented by families of polynomial endofunctors. In this setting, we show how to compute initial algebras, terminal coalgebras and another kind of fixpoint $ζ$. We then explore a number of examples of derived operators inspired by Weihrauch complexity and the usual construction of the free polynomial monad. We introduce $ζ$-expressions as the syntax of $μ$-bicomplete categories, extended with $ζ$-binders and parallel products, which thus have a natural denotation in containers. By interpreting certain $ζ$-expressions in a category of type 2 computable maps, we are able to capture a number of meaningful Weihrauch degrees, ranging from closed choice on $\{0, 1\}$ to determinacy of infinite parity games, via an "answerable part" operator.
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。
