# pullback

1. ### Basic Pullback Question

The book I'm using asks: Let φ : R → R be given by φ(t) = et . Let x be the usual coordinate function on R. Show that φ*x = ex . I can't figure this out and I don't understand why - what is the 'usual coordinate function' on R? I at first interpreted it as f(x) = x, but that doesn't make...
2. ### pullback is not the product

Does anyone know of an example of a category where the pullback is not isomorphic to the product? Any help would be appreciated.
3. ### property of pullback

Hi! Let f: M \rightarrow N a local diffeomorphism, X a vectorfield on N. We define (f^{*} X)(x):= T_x f \cdot X(x), where T_x f is the tangential map assoiciated with f. I want to show that f^{*} [X,Y]=[f^{*}X, f^{*}Y], where [.,.] is the liebracket (Y another vector field). Can anybody help me...
4. ### Self-intersection of the pullback of a hyperplane

Hey everyone, I am working on trying to figure out what is the self-intersection of the pullback of a hyperplane. In fact, I think I know the answer, I just don't know why! So here is the setup: We have a degree d finite covering Y_r of the complex projective plane \mathbb{C}P^2, with...