Kerodon

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

Definition 3.1.4.2. Let $X_{}$ and $Y_{}$ be simplicial sets, and suppose we are given a pair of morphisms $f_0, f_1: X_{} \rightarrow Y_{}$. A homotopy from $f_0$ to $f_1$ is a morphism $h: \Delta ^1 \times X_{} \rightarrow Y_{}$ satisfying $f_0 = h|_{ \{ 0\} \times X_{}}$ and $f_1 = h|_{ \{ 1\} \times X_{} }$.