_Uniqueness of universal objects._

Recall the definitions of terminal object and product from Chapter 3 in the notes.

(a) Show that if \\(t\\) and \\(t'\\) are both terminal objects in a category, then \\(t\\) and \\(t'\\) are isomorphic.

(b) Let \\(a\\) and \\(b\\) be objects of a category. Show that if \\(p\\) and \\(p'\\) are both products of \\(a\\) and \\(b\\), then they are isomorphic.

(c) Discuss the similarities between your two proofs. Could the same idea be used to show that any two initial objects are isomorphic?

***

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Recall the definitions of terminal object and product from Chapter 3 in the notes.

(a) Show that if \\(t\\) and \\(t'\\) are both terminal objects in a category, then \\(t\\) and \\(t'\\) are isomorphic.

(b) Let \\(a\\) and \\(b\\) be objects of a category. Show that if \\(p\\) and \\(p'\\) are both products of \\(a\\) and \\(b\\), then they are isomorphic.

(c) Discuss the similarities between your two proofs. Could the same idea be used to show that any two initial objects are isomorphic?

***

[Next](https://forum.azimuthproject.org/discussion/2414/question-2-5-products-in-preorders)

[Prev](https://forum.azimuthproject.org/discussion/2419/question-2-3-the-naturality-of-the-diagonal)

[All](https://forum.azimuthproject.org/categories/exercises-applied-category-theory-course)