Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 119 / 5 / b / Solution

For posets $A,B$, let $B^A$ be the poset of monotone maps $A\to B$ ordered pointwise. Evaluationis monotone. A monotone map $h:C\times A\to B$ curries to the monotone mapand this correspondence is natural and invertible. Thus the cartesian closed category of posets has exponentials $B^A$.