On the algebraic K‐theory of higher categories
On the algebraic K‐theory of higher categories
复制标题
论高范畴的代数K-理论
DOI：
10.1112/jtopol/jtv042
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发表时间：
2012
影响因子：
1.1
通讯作者：
C. Barwick
中科院分区：
文献类型：
--
作者：
C. Barwick
我们证明，当瓦尔德豪森 K 理论扩展到一类非常一般的准范畴时，可以被描述为 Goodwillie 微分。特别是，K 理论空间允许规范（联结）解环，并且 K 理论函子具有简单的普适性质。利用这一点，我们在本文中对 Waldhausen 的近似、可加性和纤维化定理给出了新的、更高的分类证明。作为这项技术的应用，我们研究了各种同伦环境中关联环的代数 K 理论以及谱 Deligne-Mumford 堆栈。
We prove that Waldhausen K ‐theory, when extended to a very general class of quasicategories, can be described as a Goodwillie differential. In particular, K ‐theory spaces admit canonical (connective) deloopings, and the K ‐theory functor enjoys a simple universal property. Using this, we give new, higher categorical proofs of the approximation, additivity, and fibration theorems of Waldhausen in this article. As applications of this technology, we study the algebraic K ‐theory of associative rings in a wide range of homotopical contexts and of spectral Deligne–Mumford stacks.