衍生子的k理论

F. Muro, G. Raptis
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引用次数: 14

摘要

我们定义了指向右导子的$K$-理论,并证明了当导子产生于一个好的Waldhausen范畴时,它与Waldhausen $K$-理论是一致的。这个$K$-理论在衍生子的一般等价下不是不变的,而只有在考虑衍生子范畴的简单充实所定义的更强的等价概念下才不变。我们证明了原来定义的导数K理论是由一个在导数等价下不变的函子对Waldhausen K理论的最佳逼近。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
K-theory of derivators revisited
We define a $K$-theory for pointed right derivators and show that it agrees with Waldhausen $K$-theory in the case where the derivator arises from a good Waldhausen category. This $K$-theory is not invariant under general equivalences of derivators, but only under a stronger notion of equivalence that is defined by considering a simplicial enrichment of the category of derivators. We show that derivator $K$-theory, as originally defined, is the best approximation to Waldhausen $K$-theory by a functor that is invariant under equivalences of derivators.
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