# Category of differential manifolds with cobordisms

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Revision as of 01:35, 28 February 2008 by Vipul (talk | contribs) (New page: {{category}} ==Definition== The '''category of differential manifolds with cobordisms''' is defined as follows: * The objects of the category are differential manifolds * The morphi...)

## Definition

The **category of differential manifolds with cobordisms** is defined as follows:

- The objects of the category are differential manifolds
- The morphisms of the category are smooth cobordisms i.e. the morphisms from to are the cobordisms from to
- Composition of morphisms is given as follows. Suppose is a smooth cobordism from to , and is a smooth cobordism from to . The cobordism from to is obtained by gluing and along the image of , and not changing the maps from and to the respective parts.