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 $\mathcal{ O}$-monoidal functor. This allows us to relate Thom spectra to $\mathbb{ E}_n$-algebras of a given characteristic in the sense of Szymik. As applications, we recover the Hopkins--Mahowald theorem realizing $H\mathbb{ F}_p$ and $H\mathbb{ Z}$ as Thom spectra, and compute the topological Hochschild homology and the cotangent complex of various Thom spectra.
Categories: math.AT