Set Category

up:: Category

The category is the category whose objects are sets and whose morphisms are functions .

Properties

• Note that, since for any set , the cardinality of the set of functions from to is , we have that is Locally Small.
• It is not a Small Category, since this would imply that the set of all sets is itself a set (which would violate Russell’s Paradox)

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References

• Set in nLab