  In this paper we give an algebraic description of the category of $n$-slices
for an arbitrary group $G$, in the sense of Hill-Hopkins-Ravenel. Specifically,
given a finite group $G$ and an integer $n$, we construct an explicit
$G$-spectrum $W$ (called an isotropic slice $n$-sphere) with the following
properties: (i) the $n$-slice of a $G$-spectrum $X$ is equivalent to the data
of a certain quotient of the Mackey functor $\underline{[W,X]}$ as a module
over the endomorphism Green functor $\underline{[W,W]}$; (ii) the category of
$n$-slices is equivalent to the full subcategory of right modules over
$\underline{[W,W]}$ for which certain restriction maps are injective. We use
this theorem to recover the known results on categories of slices to date, and
exhibit the utility of our description in several new examples. We go further
and show that the Green functors $\underline{[W,W]}$ for certain slice
$n$-spheres have a special property (they are "geometrically split") which
reduces the amount of data necessary to specify a $\underline{[W,W]}$-module.
This step is purely algebraic and may be of independent interest.
