I have a question for a reference regarding classification of covering maps on a topological set $X$ with symmetric group Čech cohomology. In Classifying Covering Spaces using First Cohomology there is already given the result:
There is a bijection between the equivalence class of $i$-sheeted covering spaces of $X$ and the first Čech cohomology with coefficients in $S_i$.
I know the classification theorem for covering spaces in Hatcher, Algebraic Topology but only on the subgroups of the fundamental group of $X$, as also mentioned in the post.
Can someone suggest a reference for the bijection to the Čech cohomology?