AI 中文总结
研究给出经典贝克单子性定理的公理同伦类似物，其在经典单子性不成立时常常成立，源于对迭代环路空间理论识别原则背景的理解，应用不同且更广泛，还通过例子为单纯集与拓扑空间等价关系提供新视角。
AI 中文摘要
我们给出了经典范畴贝克单子性定理的一个公理同伦类似物。当经典单子性不成立时它常常成立。这源于对迭代环路空间理论中识别原则的一般背景的理解，如在后续论文ArXiv 2402.03649中所处理的，但当前结果的应用不同且更广泛。一个例子为单纯集与拓扑空间之间的旧等价关系提供了新视角：两者都等价于单纯拓扑空间，且该等价关系意味着单纯空间的实现与其底层单纯集（视为离散单纯空间）的实现之间存在奇特的紧密关系。
英文摘要
We give an axiomatic homotopical analog of the classical categorical Beck monadicity theorem. It often holds when classical monadicity fails. This grew out of an understanding of a general context for recognition principles in iterated loop space theory, as treated in the logical sequel ArXiv 2402.03649, but the present result applies differently and more generally. An example gives a new perspective on the old equivalence between simplicial sets and topological spaces: both are equivalent to simplicial topological spaces, and the equivalence implies a curiously close relationship between realizations of simplicial spaces and realizations of their underlying simplicial sets, viewed as discrete simplicial spaces.
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