I am currently working through this paper and something in the author's definition of geometric realisation of an abstract simplicial complex is unclear to me:
(some stuff in between that is not relevant to us)
Namely, the condition that $\vert \tau \vert = \vert \sigma \vert + 1$ seems wrong to me...? The map $\delta_i$ sends the standard $n$-simplex to the standard $n-1$ simplex: \begin{equation*} \delta_i : \Delta^n \rightarrow \Delta^{n-1} \end{equation*} hence i would expect $\tau$ to have a smaller cardinality than $\sigma$. What am I missing here?