Hilton-Milnor's theorem in $\mathrm{\infty }$-topoi

In this note we show that the classical theorem of Hilton-Milnor on finite wedges of suspension spaces remains valid in any $\mathrm{\infty }$-topos. Our result relies on a version of James’ splitting and uses only basic constructions native to any model of $\mathrm{\infty }$-categories.