# Difference between revisions of "Category of differential manifolds with cobordisms"

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## Revision as of 01:37, 28 February 2008

This article defines a category structure on manifolds (possibly with additional structure)

View other category structures on manifolds

## 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.