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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.
   • CommentAuthornLab edit announcer
   • CommentTimeSep 1st 2022
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexPage created, but author did not leave any comments. Anonymous <a href="https://ncatlab.org/nlab/revision/flagged+category/1">v1</a>, <a href="https://ncatlab.org/nlab/show/flagged+category">current</a>

   Page created, but author did not leave any comments.

   Anonymous

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeSep 2nd 2022
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexDid we really not have this page yet? I guess not. We should also have [[flagged (infinity,1)-category]].

   Did we really not have this page yet? I guess not. We should also have flagged (infinity,1)-category.

3. • CommentRowNumber3.
   • CommentAuthorMike Shulman
   • CommentTimeSep 2nd 2022
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexNote to Anonymous: when you create a page, you should also add redirects for other names, including plural forms. I just added `[[!redirects flagged categories]]` to this page, so that links to it can write `[[flagged categories]]` rather than `[[flagged category|flagged categories]]`.

   Note to Anonymous: when you create a page, you should also add redirects for other names, including plural forms. I just added [[!redirects flagged categories]] to this page, so that links to it can write [[flagged categories]] rather than [[flagged category|flagged categories]].

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeSep 18th 2022
   • (edited Sep 18th 2022)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have - added clarification that the mysterious sounding "surjection to the underlying groupoid" is nothing but an essentially surjective functor (unless you really mean something else, in which case it ought to be said) - cross-linked with *[[category with an atlas]]* - added pointer to: * [[David Ayala]], [[John Francis]], Def. 0.12 of: *Flagged higher categories*, in: *Topology and Quantum Theory in Interaction*, Contemporary Mathematics **718**, AMS (2018) &lbrack;[arXiv:1801.08973](https://arxiv.org/abs/1801.08973), [ISBN:978-1-4704-4941-4](https://bookstore.ams.org/conm-718)&rbrack; I realize that I must have not been in the loop when this terminology decision emerged: The surprise in [#2](#Comment_102560) above refers to which earlier discussion of "flagged"? I find that the term "flag" makes good sense in the generality in which Ayala & Francis comnsider it (at least their usage is fairly analogous to the established use of *[[flags]]* in linear spaces), but here in this entry where only a single stage appears it may remain mysterious to the novice reader. Would be good to expand on this and/or add references. <a href="https://ncatlab.org/nlab/revision/diff/flagged+category/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/flagged+category/3">v3</a>, <a href="https://ncatlab.org/nlab/show/flagged+category">current</a>

   I have

   • added clarification that the mysterious sounding “surjection to the underlying groupoid” is nothing but an essentially surjective functor (unless you really mean something else, in which case it ought to be said)

   • cross-linked with category with an atlas

   • added pointer to:

     • David Ayala, John Francis, Def. 0.12 of: Flagged higher categories, in: Topology and Quantum Theory in Interaction, Contemporary Mathematics 718, AMS (2018) [arXiv:1801.08973, ISBN:978-1-4704-4941-4]

   I realize that I must have not been in the loop when this terminology decision emerged: The surprise in #2 above refers to which earlier discussion of “flagged”?

   I find that the term “flag” makes good sense in the generality in which Ayala & Francis comnsider it (at least their usage is fairly analogous to the established use of flags in linear spaces), but here in this entry where only a single stage appears it may remain mysterious to the novice reader. Would be good to expand on this and/or add references.

   diff, v3, current

5. • CommentRowNumber5.
   • CommentAuthorGuest
   • CommentTimeSep 18th 2022
   • PermaLink
   Author: Guest
   Format: MarkdownItexThis article was created because there was a link to the then non-existing [[flagged category]] article in the [[gaunt category]] article.

   This article was created because there was a link to the then non-existing flagged category article in the gaunt category article.