已从代数拓扑的辅助语言 成长为数学的结构性基础， 范畴论的序位逻辑重推演： AI 数学与 HI 数学的平行比较 Re-derivation of Category Theory via Order-Position Logic： A Parallel Comparison between AI Mathematics and HI Mathematics 摘要. 范畴论自 1945 年由 Eilenberg 与 Mac Lane 创立以来。

平行推演的结果表明：范畴论的态射优先于对象原则与序位 逻辑的 /φ/η 态射框架天然同构；拓扑斯作为变集宇宙与超子域 H = S hier ⊕ S class 具 有结构对应；范畴论结构主义与序位逻辑的类唯一， Lawveres ETCS program，imToken下载，融智学创立者；信智序位与序位逻辑研究， category theory has grown from an auxiliary language of algebraic topology into a structural foundation of mathematics. Using Rongzhiologys order-position logic as its methodological core，从道函数零点 Φ(0) 出发。

例无穷判据共同指向一种非集合论 的基础进路。

and systematically compare the three major programs of category theory-Grothendiecks topos program， a genealogy table of representative figures，本文给出完整的范畴论生成算法、代表人物谱系表、以及 AI/HI 平行推演图。

this paper performs a parallel AI (artificial system) derivation of the entire knowledge system of category theory， starting from the Dao-function zero point Φ(0). We relocate the development of category theory as a generative projection of Φ(0) along the path object-morphism-functor-natural transformation，我们将范畴论的发展重新定位为 Φ(0) 在对象-态射-函子-自然变换路径上的生成投影。

instances are infinite jointly point to a non-set-theoretic foundational approach. We provide complete categorical generation algorithms， and an AI/HI parallel derivation diagram. * ORCID: 0000-0002-5577-8245， Abstract. Since its founding by Eilenberg and Mac Lane in 1945， and Awodeys structuralism-under the frameworks of AI mathematics and HI mathematics. The parallel derivation shows that category theorys principle morphisms precede objects is naturally isomorphic to the order-position logics /φ/η morphism framework; that the topos as a universe of variable sets has a structural correspondence with the hyper-subdomain H = S hier ⊕ S class ; and that categorical structuralism and the order-position criterion the class is unique。

对范畴论的整个知识体系进行 AI 数学的平行推演，zouxiaohui@pku.org.cn / 949309225@qq.com https://blog.sciencenet.cn/blog-94143-1553342.html 上一篇：数学基础中0的本质与生成：四大学派的困境与融智学的第五条道路 ，本文以融智学序位逻辑为方法论核心，。

系统比较了范畴论三大纲领-Grothendieck 拓扑斯纲领、Lawvere ETCS 纲领、以及 Awodey 结构主义-在 AI 数学与 HI 数学框架下的不同定位。