The constant presheaf of a set $𝑋$ on a category $𝐶$ is a functor $\mathrm{\Delta }(𝑋):{𝐶}^{𝑜𝑝}\to \text{𝐒𝐞𝐭}$ such that

I often call this the discrete presheaf for $𝑋$, but I don’t know if that’s standard.