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 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 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 nforum 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 sheaves 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).

nLab > Latest Changes: Initiality Project - Semantics

Bottom of Page

1 to 9 of 9

  1.  
    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeOct 26th 2018

    Page created, but author did not leave any comments.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeOct 28th 2018

    CwFs should have a terminal object.

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorpcapriotti
    • CommentTimeOct 30th 2018

    Completed definition of CwF morphism. I also added some equivalent formulations of representability of a natural transformation in terms of categories of elements, which I think makes it slightly easier to express the strict compatibility condition on morphisms.

    diff, v4, current

    • CommentRowNumber4.
    • CommentAuthorAli Caglayan
    • CommentTimeOct 30th 2018
    • (edited Oct 30th 2018)

    What are the references for CwF? Is it just Awodey’s paper?

    • CommentRowNumber5.
    • CommentAuthorAli Caglayan
    • CommentTimeOct 30th 2018
    • (edited Oct 30th 2018)

    I found this on the HoTT wiki for anybody else interested: semantics (homotopytypetheory).

    It says:

    Categories with Families

    Classically equivalent to CwA’s, but formulated slightly differently to be better-suited to formalisation. It can also be seen as a variable-free presentation of Martin-Lof’s substitution calculus.

    What does this even mean?

    • CommentRowNumber6.
    • CommentAuthorMike Shulman
    • CommentTimeOct 30th 2018

    Beats me. (-:

    • CommentRowNumber7.
    • CommentAuthorAli Caglayan
    • CommentTimeDec 22nd 2018
    • (edited Dec 22nd 2018)

    changed to subscript, given thats what was written just above. Also talked about the horizontal maps of the diagram for CwF morphism.

    diff, v6, current

    • CommentRowNumber8.
    • CommentAuthorAli Caglayan
    • CommentTimeDec 22nd 2018
    • (edited Dec 22nd 2018)

    In CwF morphism it says A:yΓ→CA : y\Gamma \to C but shouldn’t this be A:yΓ→TyA : y \Gamma \to Ty?

    I’ve corrected it now.

    • CommentRowNumber9.
    • CommentAuthorjonsterling
    • CommentTimeDec 31st 2018
    Alizter, I believe the correct reference for cwfs is Peter Dybjer's "Internal Type Theory": http://www.cse.chalmers.se/~peterd/papers/InternalTT.pdf

    In some slides in 2012, Marcelo Fiore proposed a more categorical presentation of the notion of cwf in terms of representability (https://www.cl.cam.ac.uk/~mpf23/talks/ICALP2012.pdf); in 2016, Steve Awodey (independently) contributed a similar presentation called Natural Models, working out the details in his paper here: https://arxiv.org/pdf/1406.3219.pdf.

1 to 9 of 9

  1.