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.
    • CommentAuthorMike Shulman
    • CommentTimeOct 28th 2018

    Created, mainly with stuff from the overview.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeOct 28th 2018

    Add the clauses for variables

    v1, current

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeOct 28th 2018

    Add partial interpretation of contexts.

    v1, current

    • CommentRowNumber4.
    • CommentAuthordlicata335
    • CommentTimeNov 1st 2018

    To what extent is this proof of initiality intended to be constructive? I think that has some bearing on how the partial interpretations are treated. I think it should be possible to prove initiality in a constructive metalanguage, but maybe some shortcuts helpful for the intended audience are possible classically.

    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTimeNov 1st 2018

    I don’t immediately see anything that would make it nonconstructive.

    • CommentRowNumber6.
    • CommentAuthorMike Shulman
    • CommentTimeNov 1st 2018

    In particular, I think all the definitions of the partial interpretations should be expressed in purely category-theoretic language in the presheaf category [C op,Set][C^{op},Set], which is inherently constructive, especially because the internal logic of this category is not classical. Is there something that looks nonconstructive to you?

    • CommentRowNumber7.
    • CommentAuthorAli Caglayan
    • CommentTimeNov 8th 2018

    What exactly is Tm V\Tm^{V} where VV is a finite set?

    • CommentRowNumber8.
    • CommentAuthorMike Shulman
    • CommentTimeNov 8th 2018

    The VV-indexed power (for SetSet-enrichment) of the presheaf TmTm.

    • CommentRowNumber9.
    • CommentAuthorMike Shulman
    • CommentTimeNov 8th 2018

    Otherwise known as the product of VV copies of TmTm, or VTm\prod_{V} Tm.