  The operation of zig-zag products of graphs is the analogue of the semidirect
product of groups. Using this observation, we present a categorical description
of zig-zag products in order to generalize the construction for the category of
simple graphs. Also, we examine the covering properties of zig-zag products and
we utilize these results to estimate their spectral invariants in general. In
addition, we provide specific spectral analysis for some such products.
