Initial objects as adjoints

Remark 21.2.3. For an object \(x\) of \(C\), it follows from Corollary 21.2.2 that \(X\) is terminal if and only if the functor \[ x\colon * \to C \] is right adjoint to the functor \(p_C\colon C \to *\). Dually, \(x\) is initial if and only if it is left adjoint to \(p_C\colon C \to *\).