Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

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 comma 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 finite 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 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 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

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthormaxsnew
    • CommentTimeAug 7th 2022

    Init this page, which is referenced quite a few times. I’m not much of an expert on these weak foundations so if someone else would like to fill in some details that would be nice.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorjonsterling
    • CommentTimeAug 7th 2022

    Thanks for starting this. It would be really great to use this page to clarify a lot of misconceptions. For instance, it is sometimes said that unique choice holds in any lex category — I think there is a sense in which this is true, but it is not at all the pertinent sense.

    • CommentRowNumber3.
    • CommentAuthormaxsnew
    • CommentTimeSep 2nd 2022

    Discuss the relationship to adjunctions in Rel and how adjunctions in Prof do not satisfy the analogous property.

    I guess the analogous statement for preorders needs a form of choice (and doesn’t if they are posets). What about groupoids?

    diff, v2, current

    • CommentRowNumber4.
    • CommentAuthorGuest
    • CommentTimeSep 2nd 2022

    this mathoverflow question might be useful

    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTimeSep 3rd 2022

    Renamed to “principle of unique choice”

    diff, v3, current

    • CommentRowNumber6.
    • CommentAuthorMike Shulman
    • CommentTimeSep 3rd 2022

    A quasitopos has (at least) two “internal languages”, one that satisfies unique choice and one that doesn’t.

    I’m curious what you had in mind about lex categories, Jon. It does seem to me that the most obvious formulation of unique choice in an arbitrary lex category is the one using arbitrary subobjects, and that one holds.

    diff, v3, current

  1. added a section on the principle of unique choice in type theory


    diff, v4, current

    • CommentRowNumber8.
    • CommentAuthormaxsnew
    • CommentTime7 days ago

    redirect “function comprehension principle”

    diff, v9, current