Example 4.2.4.6. The inclusion map $i_0: \{ 0\} \hookrightarrow \Delta ^1$ is left anodyne (and therefore anodyne). However, it is not right anodyne (and therefore not inner anodyne). This follows from Proposition 4.2.4.5, since the lifting problem
\[ \xymatrix@R =50pt@C=50pt{ \{ 0\} \ar [r]^-{\operatorname{id}} \ar [d]^{i_0} & \{ 0\} \ar [d]^{i_0} \\ \Delta ^1 \ar [r]^-{\operatorname{id}} \ar@ {-->}[ur] & \Delta ^1 } \]
does not admit a solution (note that the inclusion map $i_0: \{ 0\} \hookrightarrow \Delta ^1$ is a right fibration; see Warning 4.2.1.6).