Kerodon

Corollary 4.8.5.24. Let $f: X \rightarrow Y$ be a morphism of Kan complexes and let $n$ be an integer. Then:

• The morphism $f$ is $n$-connective (in the sense of Definition 3.5.1.13) if and only if it is $m$-full for every nonnegative integer $m \leq n$.

• The morphism $f$ is $n$-truncated (in the sense of Definition 3.5.9.1) if and only if it is $m$-full for every nonnegative integer $m \geq n+2$.