From Hopf Algebras in Model Categories to Hopf Algebras in $\mathrm{\infty }$-categories

We show that algebra objects in model categories can be transferred to algebra objects in $\mathrm{\infty }$-categories, without any cofibrancy or fibrancy assumptions on the algebra. We furthermore show under some mild extra assumptions that this correspondence extends to commutative bialgebras and to commutative Hopf algebras.