3 problems

Let $s\mathscr{S}\mathrm{et}$ be the category of simplicial sets, $s\mathscr{S}\mathrm{et}^+$ the category of marked simplicial sets, and $s\mathscr{S}^+$ the category of simplicia…

The homotopy-inverse conjecture. The map $\tau$ is a homotopy inverse to $\pi$.

Parametrized classifying-space homeomorphism conjecture. The methods of Barratt and Heath adapt to give a homeomorphism