  We study simplicial profinite groups with a view towards applications in
profinite combinatorial group theory. This approach provides a natural
framework to the concept of pro-$\mathfrak{C}$-presentation of a
pro-$\mathfrak{C}$-group $G$ as a 1-truncation of its free simplicial
pro-$\mathfrak{C}$-resolution. The category of simplicial
pro-$\mathfrak{C}$-groups has a closed simplicial model category structure.
This yields a possibility to define some old and new derived functors as left
Quillen derived functors from this simplicial model category. When
$\mathfrak{C}$ is L-groups, than may construct free simplical pro-L-resolution
functorially. We introduce settings of $\Delta$-adic and Zassenhaus filtrations
for free simplical pro-p-resolutions and derive some calculations for
pro-p-groups. The usage of pro-p-Curtis-Rector spectral sequences sheds
homotopical light on Golod-Shafarevitch type results.
