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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 galois-theory 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 k-theory lie-theory limits linear linear-algebra locale localization logic mathematics 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 planar 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

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeOct 8th 2010

    promted by demand from my Basic-Course-On-Category-Theory-Students I expanded the entry 2-category:

    • mentioned more relations to other concepts in the Idea-section;

    • added an Examples-section with a bunch of (classes of) examples;

    • added a list of references. Please add more if you can think of more!

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeOct 8th 2010

    What is the purpose of the bullet list containing category, 2-category, etc. at the top of the article? It looks weird to me there – shouldn’t a page called “2-category” start with the contents of itself? Those seem more like they would go in a “related pages” section at the bottom of the page.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeOct 8th 2010

    Does it look weird?

    Darn, I thought it was a good idea. Will have to remove these, then. I keep having this urge of putting pages into context. For cases where we have sequences of pages that all vary on the same theme, I started to collect their titles in short lists at the top of the page, kind of as a sort of little menu to choose from.

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeOct 9th 2010

    I thought that putting pages in context was one of the purposes of the floating contents links on the side.

    • CommentRowNumber5.
    • CommentAuthorTim_Porter
    • CommentTimeOct 9th 2010

    @Urs. Perhaps that list could go elsewhere. I did think that it was not helpful where it is.

    • CommentRowNumber6.
    • CommentAuthorFinnLawler
    • CommentTimeOct 9th 2010

    Those lists do look a bit strange at the very beginning of the page. They are a good idea, though, I think, and they complement the subject-contents links by grouping pages more by conceptual similarity than by usage.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeOct 10th 2010

    Okay, will start moving these lists elsewhere!

    Finn wrote:

    They are a good idea, though, I think, and they complement the subject-contents links by grouping pages more by conceptual similarity than by usage.

    That had been my feeling, that the floating TOC serves to set the scene, but does not convey the immediate idea “this entry is only one variant of a single concept, the other variants of which are…”. I felt we have a bunch of entries that in principle could be on a single page.

    • CommentRowNumber8.
    • CommentAuthorzskoda
    • CommentTimeOct 11th 2010
    • (edited Oct 11th 2010)

    Darn, I thought it was a good idea. Will have to remove these, then. I keep having this urge of putting pages into context.

    I also like to have the main content straight away without scrolling, while side links on the side (like floating contents) or at the bottom of the page along with references (related entries). Many times I was writing Literature and links or References and other entries or alike section at the bottom. So I think all that idea of adding more links ios always good but not at the beginning of the entry.

    "this entry is only one variant of a single concept, the other variants of which are..."

    There are so many variant of this statement of different flavour, like related concepts, synonyms, closely related concepts, other formalisms for the same idea etc. each of these is a different flavour. If one is putting just a list with some default meaning of the list one does not know which variant of list of variants one is giving. So it is difficult to colaborate on creating such lists. Sometimes a single top page title like algebraic theories above PRO may be worthy, but one can have several groups of titles with common intersection, and each group is defined by a different principle. So I do not see a way for one size to fit all. So maybe it would be better to have explicit explanation of a compact linear list at the bottom with references.

    • CommentRowNumber9.
    • CommentAuthorTobyBartels
    • CommentTimeOct 14th 2010

    I don’t like these either and keep meaning to ask about them. Or rather, I like them very much! Just not where they are.

    Since they’re so short, maybe you can put them on the side above the other lists of contents, but without the funky code to make it disappear?

    • CommentRowNumber10.
    • CommentAuthorThomas Holder
    • CommentTimeFeb 17th 2020

    Added a reference to the recent monograph by Johnson&Yau.

    diff, v39, current

  1. Linked to category 2Cat.

    diff, v42, current

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeSep 28th 2021

    added pointer to:

    (which is a textbook on 2-category theory in itself)

    diff, v47, current

    • CommentRowNumber13.
    • CommentAuthorvarkor
    • CommentTimeOct 7th 2022

    Added reference to term “hypercategory”.

    diff, v50, current

    • CommentRowNumber14.
    • CommentAuthorvarkor
    • CommentTimeOct 20th 2022

    An anonymous editor added the term “monoidal monoidoidoid” to the page without leaving a comment. I do not think this terminology is helpful to have on the page, both because the terminology does not appear anywhere, and because it is ambiguous: it relies on the term being parsed as “(monoidal monoidoid)oid” rather than “monoidal (monoidoidoid)”, which is not the natural reading. It does not help the nLab’s reputation for obscurity when people add terms like this jokingly.

    • CommentRowNumber15.
    • CommentAuthorUrs
    • CommentTimeOct 21st 2022

    Absolutely. It could be worthwhile to add a remark explaining how such terms could come about, but just dropping them like this is no good. I have deleted it.

    diff, v51, current

    • CommentRowNumber16.
    • CommentAuthorvarkor
    • CommentTimeDec 9th 2022

    Added link to opposite 2-category.

    diff, v52, current

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