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# Exercise 76 - Chapter 3

edited June 2018

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\$$.