AI 中文总结
研究动机稳定同伦理论中悬架谱与零阶空间函子伴随的同伦单子性定理，通过验证满足一般单子性定理假设来证明，过程中展示六个单纯动机同伦理论结果及相关单子框架，或为动机无限环空间猜想提供工具。
AI 中文摘要
我们证明了动机稳定同伦理论中悬架谱与零阶空间函子之间伴随的同伦单子性定理。我们的证明验证了动机稳定同伦理论满足arXiv:2607.12124中一般单子性定理的假设。在此过程中，我们展示了单纯动机同伦理论中的六个初步结果，主要技术成分是零阶空间函子与单纯动机谱实现之间的弱交换性定理。我们还阐述了关于单子的 oplax 映射下单子代数的一般框架。这些单纯结果及伴随的单子框架可能为动机无限环空间的猜想操作识别原则提供工具。
英文摘要
We prove a homotopical monadicity theorem for the adjunction between the suspension spectrum and zeroth space functors in motivic stable homotopy theory. Our proof verifies that motivic stable homotopy theory satisfies the hypotheses of the general monadicity theorem of arXiv:2607.12124. In the process, we demonstrate six preliminary results in simplicial motivic homotopy theory, the main technical ingredient being a weak commutativity theorem between the zeroth space functor and realization of simplicial motivic spectra. We also elaborate on a general framework relating monadic algebras under op-lax maps of monads. This monadic framework is used in the proof of the main results and may be of independent interest as well. These simplicial results, and the accompanying monadic framework, may provide tools toward a conjectured operadic recognition principle for motivic infinite loop spaces.
