  We prove that algebraic de Rham cohomology as a functor defined on smooth
$\mathbb{F}_p$-algebras is formally \'etale in a precise sense. This result
shows that given de Rham cohomology, one automatically obtains the theory of
crystalline cohomology as its unique functorial deformation. To prove this, we
define and study the notion of a pointed $\mathbb{G}_a^{\mathrm{perf}}$-module
and its refinement which we call a quasi-ideal in
$\mathbb{G}_a^{\mathrm{perf}}$ -- following Drinfeld's terminology. Our main
constructions show that there is a way to "unwind" any pointed
$\mathbb{G}_a^{\text{perf}}$-module and define a notion of a cohomology theory
for algebraic varieties. We use this machine to redefine de Rham cohomology
theory and deduce its formal \'etalness and a few other properties.
