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The functor maps the set to a list of elements (this is not clearly always possible, see Are all sets totally ordered ?Are all sets totally ordered ?), but there is no problem with uniqueness.

The functor maps the set to a list of elements (this is not clearly always possible, see Are all sets totally ordered ?), but there is no problem with uniqueness.

The functor maps the set to a list of elements (this is not clearly always possible, see Are all sets totally ordered ?), but there is no problem with uniqueness.

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Igor Rivin
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The functor maps the set to a list of elements (this is not clearly always possible, see Are all sets totally ordered ?), but there is no problem with uniqueness.