Category of differential manifolds with cobordisms
This article defines a category structure on manifolds (possibly with additional structure)
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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.
All the morphisms in this category are isomorphisms.
A related notion is the 2-category of differential manifolds with smooth maps and smooth cobordisms.