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${{H}^{1}}$ and the Étale Van Kampen Theorem
Generalized étale homotopy pro-groups 
$\pi _{1}^{\acute{e}t}(C, x)$ associated with pointed, connected, small Grothendieck sites 
$(C, x)$ are defined, and their relationship to Galois theory and the theory of pointed torsors for discrete groups is explained.
Applications include new rigorous proofs of some folklore results around 
$\pi _{1}^{\acute{e}t}(\acute{e}t(X) x)$, a description of Grothendieck's short exact sequence for Galois descent in terms of pointed torsor trivializations, and a new étale van Kampen theorem that gives a simple statement about a pushout square of pro-groups that works for covering families that do not necessarily consist exclusively of monomorphisms. A corresponding van Kampen result for Grothendieck's profinite groups 
$\text{ }\!\!\pi\!\!\text{ }_{1}^{\text{Gal}}$ immediately follows.
