nLab
SimpAb

$SimpAb$ 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 ${\Delta }^{\mathrm{op}}$ of the simplex category $\Delta$ to $\mathrm{Ab}$:

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

category: category