product of posets

Let $P, Q$ be posets. We define the product of posets to be the product in the category of posets. Concretely, it is the pair $(a, b)$ for $a \in A, b \in B$ with the relation

(a, b) \leq (a^{'}, b^{'}) ⟺ a \leq a^{'} and b \leq b^{'}

product of posets

Examples