  In this paper the relative recognition principle will be proved. It states
that a pair of spaces $(X_o,X_c)$ is weakly equivalent to
$(\Omega^N_\text{rel}(\iota:B\hookrightarrow Y),\Omega^N(Y))$ if and only if
$(X_o,X_c)$ are grouplike $\overline{\mathcal{SC}^N}$-spaces, where
$\overline{\mathcal{SC}^N}$ is any cofibrant resolution of the Swiss-cheese
2-operad $\mathcal{SC}^N$. This principle will be proved for connected
$\overline{\mathcal{SC}^N}$-spaces, and also for grouplike
$\overline{\mathcal{SC}^N}$-spaces for $2<N\leq\infty$, in the form of an
equivalence of homotopy categories.
