dual category in a sentence

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  1. An example of self-dual category is the category of Hilbert spaces.
  2. There are the ideas of opposite category and dual category.
  3. The categorical dual of a monomorphism is an epimorphism, i . e . a monomorphism in a category " C " is an epimorphism in the dual category " C " op.
  4. As is clear from the symmetry of the definitions, it is a self-dual category : it is equivalent ( in fact isomorphic ) to its dual, the category obtained by reversing all the maps.
  5. An example of a self-dual category that is not *-autonomous is finite linear orders and continuous functions, which has * but is not autonomous : its dualizing object is the two-element chain but there is no tensor product.

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