Generalizations of Loday's assembly maps for Lawvere's algebraic theories
Generalizations of Loday's assembly maps for Lawvere's algebraic theories
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劳维尔代数理论洛迪装配图的推广
DOI：
10.1017/s1474748022000603
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发表时间：
2023
影响因子：
0.9
通讯作者：
Szymik, Markus
中科院分区：
文献类型：
--
作者：
Bohmann, Anna Marie;Szymik, Markus
Loday的装配映射通过系数环的K-理论和群的相应的同调逼近群环的K-理论。我们提出了一个概括，把这两个成分在同一个立足点。基于Elmendorf-Mandell的乘法性结果和我们以前的工作，我们证明了Lawvere理论的K-理论是松弛幺半群。这一结果使得我们可以在不使用更高类别语言的情况下以用户友好的方式呈现我们的理论。它还使我们能够将这个想法扩展到新的背景，并建立非阿贝尔插值方案，从而提出新的问题。许多例子说明了我们的扩展范围。
Loday’sassembly maps approximate the K-theory of group rings by the K-theory of the coefficient ring and the corresponding homology of the group. We present a generalisation that places both ingredients on the same footing. Building on Elmendorf–Mandell’s multiplicativity results and our earlier work, we show that the K-theory of Lawvere theories is lax monoidal. This result makes it possible to present our theory in a user-friendly way without using higher-categorical language. It also allows us to extend the idea to new contexts and set up a nonabelian interpolation scheme, raising novel questions. Numerous examples illustrate the scope of our extension.