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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 $f:A \to C$ and $g:B \to C$ is the solution set $\{(x, y) \in A \times B \vert f(x) = g(y)\}$.

• CommentRowNumber5.
• CommentAuthorGuest
• CommentTimeApr 27th 2022

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