Degeneracy maps in topological simplices.

Question

Im trying to find a reference on how to define the degeneracy maps $\Delta^{n+1} \rightarrow \Delta^n$ making the simplices into a cosimplicial topological space. The face maps $\Delta^n \rightarrow \Delta^{n+1}$ are easy to define and now the only thing I'm missing are the degeneracy maps. Can anyone help me out?

Answer 1

You should read the classic

Bousfield, Aldridge Knight, and Daniel Marinus Kan. Homotopy limits, completions and localizations. Vol. 304. Springer Science & Business Media, 1972.

In Chapter X and Chapter VIII you will find everything you want to know. The degeneracy maps are $s^i : \Delta^{n+1} \to \Delta^n, s^i(t_0,\dots,t_{n+1}) = (t_0,\dots,t_{i-1}, t_i + t_{i+1},t_{i+2},\dots, t_{n+1})$.