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nLab > Latest Changes: wide pullback

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  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

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