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nLab > Latest Changes: pullback of differential forms

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeOct 3rd 2012
    • (edited Oct 3rd 2012)

    quick entry for pullback of differential forms, to be further expanded

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeOct 3rd 2012
    • (edited Oct 3rd 2012)

    I think there is an axiomatics where you fix what happens for functions (0-forms) and then you require that the general case of pullback commutes with the exterior differentiation of differential forms. There is a unique (linear over ground field) operation satisfying the two axioms, I think.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeOct 3rd 2012

    Yes, sure, this is part of the statement of the Properties-section.

    But I wanted an elementary statement of the pullback the way I did it which makes sense before the de Rham differential is even introduced. That’s how the development at geometry of physics proceeds.

    Of course one could decide to proceed differently.

    • CommentRowNumber4.
    • CommentAuthorGuest
    • CommentTimeApr 27th 2022

    Why does pullback of functions redirect here, rather than to the main article pullback? In set theory the pullback of functions f:A→Cf:A \to C and g:B→Cg:B \to C is the solution set {(x,y)∈A×B|f(x)=g(y)}\{(x, y) \in A \times B \vert f(x) = g(y)\}.

    • CommentRowNumber5.
    • CommentAuthorGuest
    • CommentTimeApr 27th 2022

    there is also the type theory definition of pullback of functions at pullback

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