A simple universal property of Thom ring spectra

We give a simple universal property of the multiplicative structure on the Thom spectrum of an n-fold loop map, obtained as a special case of a characterization of the algebra structure on the colimit of a lax O-monoidal functor. This allows us to relate Thom spectra to E n -algebras of a given characteristic in the sense of Szymik. As applications, we recover the Hopkins–Mahowald theorem realizing H F p and H Z as Thom spectra, and compute the topological Hochschild homology and the cotangent complex of various Thom spectra.