论文标题
光谱Waldhausen类别，$ S_ \ bullet $ -construction和Dennis Trace
Spectral Waldhausen categories, the $S_\bullet$-construction, and the Dennis trace
论文作者
论文摘要
We give an explicit point-set construction of the Dennis trace map from the $K$-theory of endomorphisms $K\mathrm{End}(\mathcal{C})$ to topological Hochschild homology $\mathrm{THH}(\mathcal{C})$ for any spectral Waldhausen category $\mathcal{C}$.我们描述了必要的技术基础，最值得注意的是，在$ \ Mathcal {C} $中，通过Moore End索引的频谱类别的频谱类别模型。这适用于定义Waldhausen的$ s _ {\ bullet} $的版本 - 光谱Waldhausen类别的构造，这对于Dennis Trace Map的此帐户至关重要。 我们的目标既是便利性又是透明度 - 我们提供了所有细节，除了证明$ \ mathrm {thh} $的添加性定理，这是理所当然的----博览会并不关心创意的创意，而是旨在为学习Dennis Trace及其基础机器提供有用的资源。
We give an explicit point-set construction of the Dennis trace map from the $K$-theory of endomorphisms $K\mathrm{End}(\mathcal{C})$ to topological Hochschild homology $\mathrm{THH}(\mathcal{C})$ for any spectral Waldhausen category $\mathcal{C}$. We describe the necessary technical foundations, most notably a well-behaved model for the spectral category of diagrams in $\mathcal{C}$ indexed by an ordinary category via the Moore end. This is applied to define a version of Waldhausen's $S_{\bullet}$-construction for spectral Waldhausen categories, which is central to this account of the Dennis trace map. Our goals are both convenience and transparency---we provide all details except for a proof of the additivity theorem for $\mathrm{THH}$, which is taken for granted---and the exposition is concerned not with originality of ideas, but rather aims to provide a useful resource for learning about the Dennis trace and its underlying machinery.
