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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.
   • CommentAuthorDavid_Corfield
   • CommentTimeJun 1st 2019
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexAdded reference to a generalization of the Karoubi envelope for [[n-categories]] in * [[Davide Gaiotto]], [[Theo Johnson-Freyd]], _Condensations in higher categories_, ([arXiv:1905.09566](https://arxiv.org/abs/1905.09566)) <a href="https://ncatlab.org/nlab/revision/diff/Karoubi+envelope/34">diff</a>, <a href="https://ncatlab.org/nlab/revision/Karoubi+envelope/34">v34</a>, <a href="https://ncatlab.org/nlab/show/Karoubi+envelope">current</a>

   Added reference to a generalization of the Karoubi envelope for n-categories in

   • Davide Gaiotto, Theo Johnson-Freyd, Condensations in higher categories, (arXiv:1905.09566)

   diff, v34, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJun 2nd 2019
   • PermaLink
   Author: Urs
   Format: MarkdownItexVery interesting to see a physicist like Davide Gaiotto coauthor an article with some substantial abstract category theory in it.

   Very interesting to see a physicist like Davide Gaiotto coauthor an article with some substantial abstract category theory in it.

3. • CommentRowNumber3.
   • CommentAuthorvarkor
   • CommentTimeMay 9th 2023
   • PermaLink
   Author: varkor
   Format: MarkdownItexAdd what I believe is the original reference for the term "Karoubi envelope". <a href="https://ncatlab.org/nlab/revision/diff/Karoubi+envelope/36">diff</a>, <a href="https://ncatlab.org/nlab/revision/Karoubi+envelope/36">v36</a>, <a href="https://ncatlab.org/nlab/show/Karoubi+envelope">current</a>

   Add what I believe is the original reference for the term “Karoubi envelope”.

   diff, v36, current

4. • CommentRowNumber4.
   • CommentAuthorvarkor
   • CommentTimeMay 9th 2023
   • PermaLink
   Author: varkor
   Format: MarkdownItexHayashi says that Karoubi introduced this construction in [K-Theory](https://doi.org/10.1007/978-3-540-79890-3), but I haven't tried to find where exactly it is introduced (and under what name).

   Hayashi says that Karoubi introduced this construction in K-Theory, but I haven’t tried to find where exactly it is introduced (and under what name).

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeMay 9th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks! (For bystanders: This comes from discussion in another thread, [here](https://nforum.ncatlab.org/discussion/4874/karoubian-category/?Focus=109378#Comment_109378)) I have added the full publication data * [[Susumu Hayashi]], Def. 1.2 in: *Adjunction of semifunctors: categorical structures in nonextensional lambda calculus*, Theoretical Computer Science **41** (1985) 95-104 &lbrack;<a href="https://doi.org/10.1016/0304-3975(85)90062-3">doi:10.1016/0304-3975(85)90062-3</a>&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/Karoubi+envelope/37">diff</a>, <a href="https://ncatlab.org/nlab/revision/Karoubi+envelope/37">v37</a>, <a href="https://ncatlab.org/nlab/show/Karoubi+envelope">current</a>

   Thanks! (For bystanders: This comes from discussion in another thread, here)

   I have added the full publication data

   • Susumu Hayashi, Def. 1.2 in: Adjunction of semifunctors: categorical structures in nonextensional lambda calculus, Theoretical Computer Science 41 (1985) 95-104 [doi:10.1016/0304-3975(85)90062-3]

   diff, v37, current

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeMay 9th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItex> Hayashi says that Karoubi introduced this construction in [K-Theory](https://doi.org/10.1007/978-3-540-79890-3), but I haven't tried to find where exactly it is introduced (and under what name). Looks to me like Hayashi must have been thinking of Teorem 6.10 in Karoubi's "K-theory". I'll add the pointer to the entry now...

   Hayashi says that Karoubi introduced this construction in K-Theory, but I haven’t tried to find where exactly it is introduced (and under what name).

   Looks to me like Hayashi must have been thinking of Teorem 6.10 in Karoubi’s “K-theory”. I’ll add the pointer to the entry now…

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeMay 9th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexAfter "appears to have been introduced in..." I have now added: > ... apparently in reference to the construction in: > * {#Karoubi78} [[Max Karoubi]], Theorem 6.10 of: *K-Theory -- An introduction*, Grundlehren der mathematischen Wissenschaften **226**, Springer (1978) &lbrack;[pdf](https://webusers.imj-prg.fr/~max.karoubi/K.book/MK.book.pdf), [doi:10.1007%2F978-3-540-79890-3](https://link.springer.com/book/10.1007%2F978-3-540-79890-3)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/Karoubi+envelope/37">diff</a>, <a href="https://ncatlab.org/nlab/revision/Karoubi+envelope/37">v37</a>, <a href="https://ncatlab.org/nlab/show/Karoubi+envelope">current</a>

   After “appears to have been introduced in…” I have now added:

   … apparently in reference to the construction in:

   • {#Karoubi78} Max Karoubi, Theorem 6.10 of: K-Theory – An introduction, Grundlehren der mathematischen Wissenschaften 226, Springer (1978) [pdf, doi:10.1007%2F978-3-540-79890-3]

   diff, v37, current