代数K理论中的线性化映射
The Linearisation Map in Algebraic K-Theory
摘要：
设X是一个点连通单纯集，其环群为G. K-理论中的线性化映射由Waldhausen定义，使用G-等变空间。本文利用集合的预层和阿贝尔群给出了X的单形范畴的另一种描述。换句话说，线性化映射仅根据X来定义，避免使用较少几何循环群。本文还包括一个比较有限的CW对象的有限cofibrantly生成的模型类别的范畴有限性与更多的几何概念。线性化映射的应用采用了X上可收缩空间的阿贝尔群对象范畴的模型结构。
英文摘要：
Let X be a pointed connected simplicial set with loop group G. The linearisation map in K-theory as defined by Waldhausen uses G-equivariant spaces. This paper gives an alternative description using presheaves of sets and abelian groups on the simplex category of X. In other words, the linearisation map is defined in terms of X only, avoiding the use of the less geometric loop group. The paper also includes a comparison of categorical finiteness with the more geometric notion of finite CW objects in cofibrantly generated model categories. The application to the linearisation map employs a model structure on the category of abelian group objects of retractive spaces over X.
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