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Exercise 76 - Chapter 3

Let \( (P, \le) \) be a preorder. Show that \( z \in P \) is a terminal object if and only if it is maximal: that is, if and only if for all \(c \in P\) we have \(c \le z\).

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  • 1.

    An object is terminal iff every object has a unique morphism into it. That is, \(\forall c\in P\,\,c\to z\Leftrightarrow c\leq z\).

    Comment Source:An object is terminal iff every object has a unique morphism into it. That is, \\(\forall c\in P\,\,c\to z\Leftrightarrow c\leq z\\).
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