The Hilton-Milnor theorem in higher topoi

In this note, we show that the classical theorem of Hilton-Milnor on finite wedges of suspension spacesremains valid in an arbitrary infinity-topos. Our result relieson a version of James' splitting proved in [Devala-purkar and Haine, Doc. Math. 26 (2021), 1423-1464] anduses only basic constructions native to any model of infinity-categories.