arXiv: Experimental full text search
KT (K-theory), CT (Category theory), AG (Algebraic Geometry)
Some results in Dwyer: Twisted homological stability…
nLab on Waldhausen category, see also S-construction
Kth
http://mathoverflow.net/questions/9319/co-homology-associated-to-waldhausen-k-theory
Thomason-Trobaugh, see Thomason folder.
Some kind of relation with Grothendieck’s derivators: Tabuada
arXiv:1204.3607 On the algebraic K-theory of higher categories, I. The universal property of Waldhausen K-theory from arXiv Front: math.KT by C. Barwick 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.
[arXiv:1212.5232] On exact infinity-categories and the Theorem of the Heart from arXiv Front: math.KT by C. Barwick We introduce a notion of exact quasicategory, and we prove an analogue of Amnon Neeman’s Theorem of the Heart for Waldhausen K-theory.
Toen: Homotopical and higher categorical structures in algebraic geometry. File Toen web unpubl hab.pdf. Treats general philosophical background, various forms of homotopy theories, Segal categories, Waldhausen Kth briefly, Hochshild cohomology of Segal categories and of model cats, S-cats, Segal topoi, Tannakian duality for Segal cats, and schematic homotopy types. Also letter to May about n-cats.
arXiv:1207.6613 Waldhausen Additivity: Classical and Quasicategorical from arXiv Front: math.AT by Thomas M. Fiore, Wolfgang Lück We give a short proof of classical Waldhausen Additivity, and then prove Waldhausen Additivity for an infinity-version of Waldhausen K-theory. Namely, we prove that Waldhausen K-theory sends a split-exact sequence of Waldausen quasicategories A –> E –> B to a stable equivalence of spectra K(E) –> K(A) v K(B) under a few mild hypotheses. For example, each cofiber sequence in A of the form a_0 –> a_1 –> * is required to have the first map an equivalence. Model structures, presentability, and stability are not needed. In an effort to make the article self-contained, we provide many details in our proofs, recall all the prerequisites from the theory of quasicategories, and prove some of those as well. For instance, we develop the expected facts about (weak) adjunctions between quasicategories and (weak) adjunctions between simplicial categories.
nLab page on Waldhausen K-theory