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 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 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: wide pullback

Bottom of Page

1 to 5 of 5

  1.  
    • CommentRowNumber1.
    • CommentAuthorGuest
    • CommentTimeMay 25th 2023

    starting discussion page

    diff, v26, current

    • CommentRowNumber2.
    • CommentAuthorGuest
    • CommentTimeMay 25th 2023

    In dependent type theory, the pullback of a pair of functions f:A→Cf:A \to C and g:B→Cg:B \to C is represented by the dependent sum type

    ∑ x:A∑ y:BId C(f(x),g(y))\sum_{x:A} \sum_{y:B} \mathrm{Id}_C(f(x),g(y))

    What happens when instead of a pair of functions with codomain CC, one has a family x:I⊢f(x):A(x)→Cx:I \vdash f(x):A(x) \to C of functions with codomain CC? In category theory the corresponding notion is a wide pullback of a family of morphisms with codomain CC. How does one represent the wide pullback of the family of functions x:I⊢f(x):A(x)→Cx:I \vdash f(x):A(x) \to C?

    • CommentRowNumber3.
    • CommentAuthorvarkor
    • CommentTimeDec 9th 2023

    Added a reference for the terminology “wide pullback”.

    diff, v27, current

  4. Moved existing section on wide pushouts in dependent type theory over to wide pushout type

    diff, v32, current

  5. Moved existing section on wide pullbacks in dependent type theory over to wide pullback type

    diff, v34, current

1 to 5 of 5

  1.