Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthoradeelkh
   • CommentTimeSep 3rd 2014
   • PermaLink
   Author: adeelkh
   Format: MarkdownItexAdded a stub at [[Waldhausen K-theory of a dg-category]]. I call this the _Waldhausen_ K-theory and not simply K-theory because I imagine that there should also be a more intrinsic definition not passing through Waldhausen categories or stable infinity-categories.

   Added a stub at Waldhausen K-theory of a dg-category. I call this the Waldhausen K-theory and not simply K-theory because I imagine that there should also be a more intrinsic definition not passing through Waldhausen categories or stable infinity-categories.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeSep 3rd 2014
   • (edited Sep 3rd 2014)
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks! I have added minimal cross-links at _[[Waldhausen K-theory]]_ and at _[[dg-category]]_. Which reminds me that the former just redirects to _[[K-theory]]_, eventually we should split that off and expand. A few weeks back in New York Clark Barwick had given us a nice perspective on his view of K-theory of Waldhausen $\infty$-categories as the "absolute" case (in the sense of absolute/$\mathbb{F}_1$-geometry) of the Cisinski-Tabuada-Gepner-... noncommutative motives, in that the latter may all be obtained by a kind of base change from the "stable Waldhausen $\infty$-category". I had wanted to give a brief survey of this story on the $n$Lab, but never got around to. The talk video is [here](http://videostreaming.gc.cuny.edu/videos/video/1804/in/channel/55/).

   Thanks! I have added minimal cross-links at Waldhausen K-theory and at dg-category.

   Which reminds me that the former just redirects to K-theory, eventually we should split that off and expand.

   A few weeks back in New York Clark Barwick had given us a nice perspective on his view of K-theory of Waldhausen $\infty$-categories as the “absolute” case (in the sense of absolute/$\mathbb{F}_1$-geometry) of the Cisinski-Tabuada-Gepner-… noncommutative motives, in that the latter may all be obtained by a kind of base change from the “stable Waldhausen $\infty$-category”.

   I had wanted to give a brief survey of this story on the $n$Lab, but never got around to.

   The talk video is here.

3. • CommentRowNumber3.
   • CommentAuthoradeelkh
   • CommentTimeSep 3rd 2014
   • PermaLink
   Author: adeelkh
   Format: MarkdownItexThat's interesting, I will take a look. Thanks!

   That’s interesting, I will take a look. Thanks!