The $mod2$ Steenrod and Dyer-Lashof algebras as quotients of a free algebra

Abstract

A non-connected neither of finite type Hopf algebra ${\mathcal{F}}_0$ is defined over $\mathbb{Z}/2\mathbb{Z}$ and its hom dual turns out to be a tensor product of polynomial algebras. Certain quotient Hopf algebras include the Steenrod and Dyer-Lashof algebras. This setting provides a map between the Steenrod coalgebra and a direct limit of Dyer-Lashof coalgebras.