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1. • CommentRowNumber1.
   • CommentAuthorDmitri Pavlov
   • CommentTimeFeb 28th 2023
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItex## Idea A generalization of [[Waldhausen K-theory]] to dualizable [[dg-categories]] and dualizable [[stable ∞-categories]]. For compactly generated inputs, recovers the [[Waldhausen K-theory]] of the full subcategory of compact objects. The formalism is applicable to $\lambda$-presentable stable ∞-categories, where $\lambda$ can be uncountable (for example, various categories of sheaves, or categories occurring in functional analysis). ## References * [[Alexander Efimov]], _On the K-theory of large triangulated categories_, ICM 2022, <https://www.youtube.com/watch?v=RUDeLo9JTro> * [[Marc Hoyois]], _K-theory of dualizable categories (after A. Efimov)_, <https://hoyois.app.uni-regensburg.de/papers/efimov.pdf>. * Li He, _Efimov K-theory and universal localizing invariant_, [arXiv:2302.13052](https://arxiv.org/abs/2302.13052). <a href="https://ncatlab.org/nlab/revision/Efimov+K-theory/1">v1</a>, <a href="https://ncatlab.org/nlab/show/Efimov+K-theory">current</a>

   Idea

   A generalization of Waldhausen K-theory to dualizable dg-categories and dualizable stable ∞-categories.

   For compactly generated inputs, recovers the Waldhausen K-theory of the full subcategory of compact objects.

   The formalism is applicable to $\lambda$-presentable stable ∞-categories, where $\lambda$ can be uncountable (for example, various categories of sheaves, or categories occurring in functional analysis).

   References

   • Alexander Efimov, On the K-theory of large triangulated categories, ICM 2022, https://www.youtube.com/watch?v=RUDeLo9JTro

   • Marc Hoyois, K-theory of dualizable categories (after A. Efimov), https://hoyois.app.uni-regensburg.de/papers/efimov.pdf.

   • Li He, Efimov K-theory and universal localizing invariant, arXiv:2302.13052.

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorDmitri Pavlov
   • CommentTimeMar 18th 2024
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexAdded a reference: Nikolaus. <a href="https://ncatlab.org/nlab/revision/diff/Efimov+K-theory/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/Efimov+K-theory/3">v3</a>, <a href="https://ncatlab.org/nlab/show/Efimov+K-theory">current</a>

   Added a reference: Nikolaus.

   diff, v3, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMar 19th 2024
   • PermaLink
   Author: Urs
   Format: MarkdownItexaccording to the pdf itself, Nikolaus is not the only author: * [[Achim Krause]], [[Thomas Nikolaus]], *Sheaves on manifolds* (2024) [[pdf](https://www.uni-muenster.de/IVV5WS/WebHop/user/nikolaus/Papers/sheaves-on-manifolds.pdf)] No?

   according to the pdf itself, Nikolaus is not the only author:

   • Achim Krause, Thomas Nikolaus, Sheaves on manifolds (2024) [pdf]

   No?

4. • CommentRowNumber4.
   • CommentAuthorDmitri Pavlov
   • CommentTimeMar 20th 2024
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexRe #3: It's a course by Thomas Nikolaus. But probably both should be listed as authors of lecture notes, since this is what is being cited.

   Re #3: It’s a course by Thomas Nikolaus. But probably both should be listed as authors of lecture notes, since this is what is being cited.

5. • CommentRowNumber5.
   • CommentAuthorDavid_Corfield
   • CommentTimeMay 21st 2024
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexAdded * [[Alexander Efimov]], _K-theory and lozalizing invariants of large categories_ &lbrack;[arXiv:2405.12169](https://arxiv.org/abs/2405.12169)&rbrack; and will add to his page. Interesting, the analogy he describes between dualizable categories and compact Hausdorff spaces in Appendix F. <a href="https://ncatlab.org/nlab/revision/diff/Efimov+K-theory/6">diff</a>, <a href="https://ncatlab.org/nlab/revision/Efimov+K-theory/6">v6</a>, <a href="https://ncatlab.org/nlab/show/Efimov+K-theory">current</a>

   Added

   • Alexander Efimov, K-theory and lozalizing invariants of large categories [arXiv:2405.12169]

   and will add to his page.

   Interesting, the analogy he describes between dualizable categories and compact Hausdorff spaces in Appendix F.

   diff, v6, current

6. • CommentRowNumber6.
   • CommentAuthorDavid_Corfield
   • CommentTimeMay 21st 2024
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexI see Efimov has a typo in his title. Assuming he'll fix this soon, I'll change it.

   I see Efimov has a typo in his title. Assuming he’ll fix this soon, I’ll change it.