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arXiv · 1402.1871

K-theory of derivators revisited

Fernando Muro·George Raptis
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Abstract

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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BibTeXRIS

Fernando Muro, George Raptis. 2016-07-14. K-theory of derivators revisited. https://doi.org/10.2140/akt.2017.2.303

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