On the algebraic K-theory of higher categories, I. The universal property of Waldhausen K-theory

Details On the algebraic K-theory of higher categories, I. The universal property of Waldhausen K-theory On the algebraic K-theory of higher categories, I. The universal property of Waldhausen K-theory

2012-04-16

arxiv.org/abs/1204.3607v1

Mathematics

K-Theory and Homology

70 pages. Comments always welcome

Scientific paper

We prove that Waldhausen K-theory, when extended to a very general class of quasicategories, can be described as a Goodwillie differential. In particular, K-theory spaces admit canonical (connective) deloopings, and the K-theory functor enjoys a universal property. Using this, we give new, higher categorical proofs of both the additivity and fibration theorems of Waldhausen. As applications of this technology, we study the algebraic K-theory of symmetric monoidal higher groupoids, higher topoi, associative ring spectra, and spectral Deligne-Mumford stacks.

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