论文标题
多字符$ k $ - 理论是同义理论的等效性
Multifunctorial $K$-Theory is an Equivalence of Homotopy Theories
论文作者
论文摘要
我们表明，从小型置换类别到$ \ MATHCAL {G} _*$ - 类别，$ \ Mathcal {G} _*$ - 简单集和缔结频谱的三个$ K $ - 理论多函数中的每个函数中的每个函数是同质理论的等价性。对于这些$ k $ Theory多函数中的每一个，我们描述了一个显式同型逆函数。作为我们对尖头图类别的一般结果的单独应用，我们观察到，右诱导的同型同质理论$ \ MATHCAL {E} _*$ - 类别与尖头的简单类别的同型理论相当。
We show that each of the three $K$-theory multifunctors from small permutative categories to $\mathcal{G}_*$-categories, $\mathcal{G}_*$-simplicial sets, and connective spectra, is an equivalence of homotopy theories. For each of these $K$-theory multifunctors, we describe an explicit homotopy inverse functor. As a separate application of our general results about pointed diagram categories, we observe that the right-induced homotopy theory of Bohmann-Osorno $\mathcal{E}_*$-categories is equivalent to the homotopy theory of pointed simplicial categories.
