Categories for the Working Mathematician
《Categories for the Working Mathematician》 · 第 236—237 页 · Chapter X, Section 3
Given functors \(K:\mathcal M\to\mathcal C\) and \(T:\mathcal M\to\mathcal A\), a right Kan extension of \(T\) along \(K\) is a pair \(R,\varepsilon:RK\to T\) consisting of a functor \(R\in\mathcal A^{\mathcal C}\) and a natural transformation \(\varepsilon\) which is universal as an arrow from \(\mathcal A^K:\mathcal A^{\mathcal C}\to\mathcal A^{\mathcal M}\) to \(T\in\mathcal A^{\mathcal M}\).