The internal Yoneda lemma for locally Cartesian closed $\infty$-categories

Abstract

We formulate and prove internal versions of the Yoneda lemma and of the Yoneda embedding theorem in a finitely complete, locally Cartesian closed $\infty$-category $\mathscr{C}$: for every object $X\in \mathscr{C}$ and every universe $\mathscr{U}$ classifying the diagonal of $X$