[Inquiry] Re: Differential And Riemannian Manifolds

[Jon Awbrey]

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DARM.  Note 16

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| 2.2.  Submanifolds, Immersions, Submersions (cont.)
|
| One can view the fiber product unsymmetrically.
| Given two morphisms f, g as in the following
| diagram:
|
|                             o Y
|                             |
|                             |
|                             |
|                             | g
|                             |
|                             |
|                             v
|       X o------------------>o Z
|                   f
|
| assume that their fiber product exists,
| so that we can fill in the diagram:
|
| X x_Z Y o------------------>o Y
|         |                   |
|         |                   |
|         |                   |
|     g_1 |                   | g
|         |                   |
|         |                   |
|         v                   v
|       X o------------------>o Z
|                   f
|
| We say that g_1 is the "pull back" of g by f, and also
| write it as f*(g).  Similarly, we write X x_Z Y as f*(Y).
|
| [The "x_Z" symbol is a cross-product "x" with a subscript "Z".]
|
| Lang, DARM, pp. 29-30.
|
| Serge Lang,
|'Differential & Riemannian Manifolds',
| Springer-Verlag, New York, NY, 1995.

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