  We present a natural and explicit multigraded minimal free resolution for
each generalized co-letterplace ideal (see Definition 1.1). Our resolution
differs significantly from the ones presented in the works of Ene et al.
\cite{EHM} and D'Al{`\i} et al. \cite{DFN}. Additionally, we show that each
power of a large class of generalized co-letterplace ideals can be represented
as the quotient of another generalized co-letterplace ideal by a regular
sequence of variable differences. Finally, we provide a new class of simplicial
spheres
