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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

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    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeDec 6th 2018

    Add references relating to rewriting.

    diff, v2, current

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeDec 7th 2018

    When should we say ’type 2-theory’ rather than ’2-type theory’?

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeDec 7th 2018

    My own inclination is to always say the former and never the latter. I really want to say “2-(type theory)” but that’s hard to pronounce correctly, while to my ear “2-type theory” sounds like “(2-type) theory” whereas “type 2-theory” is easier to understand as meaning “2-(type theory)”. But I didn’t want to rename the page unilaterally; any other opinions?

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeDec 8th 2018

    Matches ’Klein 2-geometry’ where it all began for me, so I’m in.

    • CommentRowNumber5.
    • CommentAuthorSam Staton
    • CommentTimeDec 9th 2018

    One potential source of confusion for “type 2-theory” is “type-2 theory”, e.g. Type two theory of effectivity, Type II string theory!

    • CommentRowNumber6.
    • CommentAuthorMike Shulman
    • CommentTimeDec 9th 2018

    I don’t personally hear any danger of “type-2 theory”; when I say it the space is much longer than the hyphen.

    • CommentRowNumber7.
    • CommentAuthorvarkor
    • CommentTimeOct 21st 2021

    Add reference to Saville’s PhD thesis “Cartesian closed bicategories: type theory and coherence”.

    diff, v4, current

    • CommentRowNumber8.
    • CommentAuthorvarkor
    • CommentTimeOct 21st 2021

    Added reference to Garner’s “Two-dimensional models of type theory”.

    diff, v4, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeOct 21st 2021
    • (edited Oct 21st 2021)

    Thanks.

    I have added DOI-link and author link to Garner 09 and put the article into chronological order (hence: on top of the list).

    NB: adding author link just amounts to enclosing the name in double square brackets, the rest is handled by the software.

    In situations such as here I’d urge to hyperlink the author name, because otherwise it looks like people who came 7 years after the fact took care to hyperlink their own names while not bothering to do the same favor to the original author.

    diff, v5, current

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeOct 21st 2021

    Also tried to organize the list of references into “General” and “Application to adjoint/modal logic”. But please check and adjust if necessary.

    diff, v5, current

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeJan 1st 2023

    added pointer to:

    diff, v6, current

    • CommentRowNumber12.
    • CommentAuthoranuyts
    • CommentTimeSep 19th 2024

    Citations.

    diff, v8, current

    • CommentRowNumber13.
    • CommentAuthoranuyts
    • CommentTimeSep 19th 2024

    Mention Cat as an example of a 2-category so that readers need to digest one level of abstraction fewer.

    diff, v8, current