Raptis, George (2022) Higher homotopy categories, higher derivators, and K-theory. FORUM OF MATHEMATICS SIGMA, 10. ISSN , 2050-5094
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For every infinity-category C, there is a homotopy n-category h(n)C and a canonical functor gamma(n) : C -> h(n)C. We study these higher homotopy categories, especially in connection with the existence and preservation of (co)limits, by introducing a higher categorical notion of weak colimit. Using homotopy n-categories, we introduce the notion of an n-derivator and study the main examples arising from infinity-categories. Following the work of Maltsiniotis and Garkusha, we define K-theory for infinity-derivators and prove that the canonical comparison map from the Waldhausen K-theory of C to the K-theory of the associated n-derivator D-C((n)) is (n + 1)-connected. We also prove that this comparison map identifies derivator K-theory of infinity-derivators in terms of a universal property. Moreover, using the canonical structure of higher weak pushouts in the homotopy n-category, we also define a K-theory space K(h(n)C, can) associated to h(n)C. We prove that the canonical comparison map from the Waldhausen K-theory of C to K(h(n)C, can) is n-connected.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Ulrich Bunke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 07 Nov 2023 08:52 |
| Last Modified: | 07 Nov 2023 08:52 |
| URI: | https://pred.uni-regensburg.de/id/eprint/56637 |
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