什么是对称幺半范畴？
What are symmetric monoidal categories?
AI总结：
研究对称幺半范畴，证明其2-范畴与$\sP$-伪代数及严格特殊$\sF$-伪代数的2-范畴等价，此等价为无限循环空间理论提供简化增强，有独立研究意义。
AI中文摘要：
自20世纪60年代以来，对称幺半范畴已被理解，并且在许多数学分支中处于核心地位。特别是，从对称幺半范畴构建谱是代数K理论的核心。此构建始于具有合适操作代数$\sP$作用的范畴，或始于从有限集范畴$\sF$到范畴$\mathbf{Cat}$的合适函子。编纂这些构建的无限循环空间理论导致了$\infty$-范畴的发明。本文将证明对称幺半范畴的2-范畴与$\sP$-伪代数的2-范畴以及严格特殊$\sF$-伪代数的同构2-范畴等价（实际上非常接近同构）。这种等价是无限循环空间理论的简化等变和乘法增强的基础，且具有独立的研究价值。
英文摘要：
Symmetric monoidal categories have been understood since the 1960's and are central to many branches of mathematics. In particular, the construction of spectra from symmetric monoidal categories is at the heart of algebraic $K$-theory. This construction starts from either categories with an action by a suitable operad $\sP$ or with suitable functors from the category $\sF$ of finite sets to the category $\mathbf{Cat}$ of categories. Infinite loop space theory, which codifies these constructions, led to the invention of $\infty$-categories. So why the title? We shall prove that the $2$-category of symmetric monoidal categories is equivalent (in fact very nearly isomorphic) both to a $2$-category of $\sP$-pseudoalgebras and to an isomorphic $2$-category of strictly special $\sF$-pseudoalgebras. This equivalence underlies a streamlined equivariant and multiplicative enhancement of infinite loop space theory, but it should be of independent interest.
