# Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$

Definition 3.2.6.4. Let $X$ be a simplicial set. We will say that $X$ is contractible if the projection map $X \rightarrow \Delta ^{0}$ is a homotopy equivalence (Definition 3.1.5.1). We say that $X$ is weakly contractible if the projection map $X \rightarrow \Delta ^{0}$ is a weak homotopy equivalence (Definition 3.1.5.11).