If I understand, given a function \\( f : X \rightarrow Y \\) we can find both pullbacks/preimages of both subsets \\( f_P^* : PY \rightarrow PX \\) and partitions/equivalence relations \\( f_{\mathcal{E}}^* : \mathcal{E}(Y) \rightarrow \mathcal{E}(X) \\)?