N-Truncated Object

An object X 𝑋 X in an Infinity Topos is n-truncated if the Diagonal Map X X S n + 1 𝑋 superscript 𝑋 superscript 𝑆 𝑛 1 X\to X^{S^{n+1}} is invertible. Morally, this is the same thing as saying that X 𝑋 X has H-Level n 𝑛 n