  In this short note we give an elementary description of the linear part of
the minimal free resolution of a Stanley-Reisner ring of a simplicial complex
$\Delta$. Indeed, the differentials in the linear part are simply a compilation
of restriction maps in the simplicial cohomology of induced subcomplexes of
$\Delta$.
  Along the way, we also show that if a monomial ideal has at least one
generator of degree $2$, then the linear strand of its minimal free resolution
can be written using only $\pm 1$ coefficients.
