Intrinsic Khovanov homology in ${\mathbb{R}\mathbb{P}}^3$

We prove that Khovanov homology is an invariant of links in unparametrized ${\mathbb{R}\mathbb{P}}^3$’s, i.e., oriented $3$-manifolds diffeomorphic to ${\mathbb{R}\mathbb{P}}^3$. Along the way, we establish the functoriality of Khovanov homology for link cobordisms in $I\times {\mathbb{R}\mathbb{P}}^3$.