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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.
   • CommentAuthorUrs
   • CommentTimeMay 16th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexstub for [[2-topos]] (mostly so that the links we have to it do point somewhere at least a little bit useful)

   stub for 2-topos (mostly so that the links we have to it do point somewhere at least a little bit useful)

2. • CommentRowNumber2.
   • CommentAuthorDavid_Corfield
   • CommentTimeMar 10th 2023
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexAdded the reference * [[Dominique Bourn]], _Sur les ditopos_, C. R. Acad. Sci. Paris 279, 911–913 (1974). <a href="https://ncatlab.org/nlab/revision/diff/2-topos/28">diff</a>, <a href="https://ncatlab.org/nlab/revision/2-topos/28">v28</a>, <a href="https://ncatlab.org/nlab/show/2-topos">current</a>

   Added the reference

   • Dominique Bourn, Sur les ditopos, C. R. Acad. Sci. Paris 279, 911–913 (1974).

   diff, v28, current

3. • CommentRowNumber3.
   • CommentAuthorTodd_Trimble
   • CommentTimeJun 4th 2023
   • (edited Jun 4th 2023)
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexI feel like some work (that I don't feel up to at the moment) could be put into clarifying which notions of 2-topos are being invoked in the statements at various points. For example, I expect Theorem 2.2 could be clarified, by starting off with "For $\mathcal{X}$ a 2-topos of 2-sheaves on a 2-site" (instead of just "For $\mathcal{X}$ a 2-topos") because nowhere on the page appears a definite definition of 2-topos. Anyway, the page in its current state has a waffly appearance; perhaps the state of the art has improved since it was first written.

   I feel like some work (that I don’t feel up to at the moment) could be put into clarifying which notions of 2-topos are being invoked in the statements at various points. For example, I expect Theorem 2.2 could be clarified, by starting off with “For $\mathcal{X}$ a 2-topos of 2-sheaves on a 2-site” (instead of just “For $\mathcal{X}$ a 2-topos”) because nowhere on the page appears a definite definition of 2-topos. Anyway, the page in its current state has a waffly appearance; perhaps the state of the art has improved since it was first written.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJun 4th 2023
   • (edited Jun 4th 2023)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added that assumption of "2-sheaf 2-topos" to the theore ([here](https://ncatlab.org/nlab/show/2-topos#2SheavesAsInternalCategories)). My vague memory is that this theorem was formulated in order to condense the implication of the two theorems cited in the proof. Following the link to these, the assumptions are stated more clearly. (Not that I disagree that this entry, like most, would deserve to be improved.) While at it, I have added the publication data for this reference: * [[Mark Weber]], *Yoneda structures from 2-toposes*, Appl Categor Struct **15** (2007) 259–323 &lbrack;[doi:10.1007/s10485-007-9079-2](https://doi.org/10.1007/s10485-007-9079-2), [pdf](https://sites.google.com/site/markwebersmaths/home/yoneda-structures-from-2-toposes)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/2-topos/29">diff</a>, <a href="https://ncatlab.org/nlab/revision/2-topos/29">v29</a>, <a href="https://ncatlab.org/nlab/show/2-topos">current</a>

   I have added that assumption of “2-sheaf 2-topos” to the theore (here). My vague memory is that this theorem was formulated in order to condense the implication of the two theorems cited in the proof. Following the link to these, the assumptions are stated more clearly.

   (Not that I disagree that this entry, like most, would deserve to be improved.)

   While at it, I have added the publication data for this reference:

   • Mark Weber, Yoneda structures from 2-toposes, Appl Categor Struct 15 (2007) 259–323 [doi:10.1007/s10485-007-9079-2, pdf]

   diff, v29, current

5. • CommentRowNumber5.
   • CommentAuthorDavid_Corfield
   • CommentTimeJan 31st 2024
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexAdded * [[Luca Mesiti]], _2-classifiers via dense generators and Hofmann-Streicher universe in stacks_ &lbrack;[arXiv:2401.16900](https://arxiv.org/abs/2401.16900)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/2-topos/30">diff</a>, <a href="https://ncatlab.org/nlab/revision/2-topos/30">v30</a>, <a href="https://ncatlab.org/nlab/show/2-topos">current</a>

   Added

   • Luca Mesiti, 2-classifiers via dense generators and Hofmann-Streicher universe in stacks [arXiv:2401.16900]

   diff, v30, current