nLab
SimpSet

$\mathrm{Simp}\mathrm{Set}$, or $\mathrm{SSet}$ for short, is the category of simplicial sets.

This is the functor category from the opposite category ${\Delta }^{\mathrm{op}}$ of the simplex category $\Delta$ to the category Set of sets:

$$\mathrm{Simp}\mathrm{Set}:=[{\Delta }^{\mathrm{op}},\mathrm{Set}].$$Simp Set := [\Delta^{op}, Set] \,.

$\mathrm{Simp}\mathrm{Set}$ is naturally a model category using the model structure on simplicial sets.

category: category