Assume every category of elements of a representable presheaf is a preorder. Let
$$
P=\coprod_{A\in\operatorname{ob}\mathcal C}(1\downarrow\mathcal C(-,A)).
$$
A disjoint union of preorders is a preorder. The category-of-elements projection $P\to\mathcal C$ is a <discrete fibration>. It is surjective on objects because $B\in\mathcal C$ is the image of the object $1_B:B\to B$ in the summand indexed by $B$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 119 / 1 / c / ii / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/iii/paper-119/1/c/ii/solution