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Let CGWH be the category of weak Hausdorff compactly generated spaces; see e.g. N.P. Strickland. THE CATEGORY OF CGWH SPACES: Preprint available from https://neil-strickland.staff.shef.ac.uk/courses/...

The following statement should be immediately implied by Eilenberg–Zilber theorem if the sequences $(i_0,\ldots,i_k)$ below are only monotone. But I need the strict monotone version which I believe to ...

Let $\mathcal{C}$ be a simplicial category, and let $N(\mathcal{C})$ be its simplicial nerve. We can form the category of twisted arrows as a simplicial category $TwArr(\mathcal{C})$ Now Lurie's ...

Given a bisimplicial manifold (or set, topological space) there is the bar construction, which assigns to it a simplicial manifold, called the total simplicial manifold. Now stepping back for a moment,...