Basic Category Theory
《Basic Category Theory》 · 第 100 页 · Corollary 4.3.3
A representation of \(X:\mathcal A\to\mathbf{Set}\) consists of an object \(A\) and an element \(u\in X(A)\) such that for every \(B\) and \(x\in X(B)\) there is a unique map \(\bar x:A\to B\) with \((X\bar x)(u)=x\).