We present an overview of a result by Yuli{\u\i} Andreevich Dubinski{\u\i} [Mat.~Sb. 67 (109) (1965); translated in Amer.~Math.~Soc.~Transl. (2) 67 (1968)], concerning the compact embedding of a seminormed set in $L^p(0,T;\cA_0)$, where $\mathcal{A}_0$ is a Banach space and $p\in[1,\infty]$; we establish a variant of Dubinski{\u\i}'s theorem, where a seminormed nonnegative cone is used instead of a seminormed set; and we explore the connections of these results with a nonlinear compact embedding theorem due to Emmanuel Maitre [Int.~J.~Math. Math. Sci. 27 (2003)].