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Initial Objects

Brooks Mershon edited this page Nov 21, 2016 · 3 revisions

From nothing there was everything.

Initial Object

An initial object in some category has the property that there is exactly one map from it to the other objects in the category.

Fun facts:

  • Two initial objects in a category necessarily have an isomorphism between them, and that isomorphism is unique.
  • In the category of sets, the initial object is the empty set.
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