nLab
SimpAb

$\Simp\Ab$ is the category of simplicial abelian groups, i.e., of simplicial objects in the category Ab of abelian groups, i.e., it is the functor category of functors from the opposite category $\Delta^{op}$ of the simplex category $\Delta$ to $Ab$:

$$\Simp\Ab = [\Delta^{op}, Ab] \,.$$

category: category