symmetric monoidal (∞,1)-category of spectra
An element $x\in C$ in a coalgebra (or, more generally coring) $(C,\Delta,\epsilon)$ is primitive if $\Delta(x) = 1\otimes x + x\otimes 1$ and $\epsilon(x) = 0$. By Milnor-Moore theorem, for Hopf algebras over a field of characteristics zero, the subspace of primitive elements generates a subalgebra which is isomorphic to the enveloping algebra of some Lie algebra.