A map f : X → Y : 𝑓 → 𝑋 𝑌 f:X\to Y 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.