Given $\mathcal{I}$ an ideal over $\mathbb{R}$, there are four main associated invariants:
$\mathrm{add}(\mathcal{I}) = \min\{|\mathcal{A}|\ :\ \mathcal{A}\subseteq \mathcal{I}\ \wedge\ \bigcup \mathcal{A} \notin \mathcal{I}\}$
$\mathrm{cov}(\mathcal{I}) = \min\{|\mathcal{A}|\ :\ \mathcal{A}\subseteq \mathcal{I}\ \wedge\ \bigcup \mathcal{A} = \mathbb{R}\}$
$\mathrm{non}(\mathcal{I}) = \min\{|X|\ :\ X\subseteq \mathbb{R}\ \wedge\ X \notin \mathcal{I}\}$
$\mathrm{cof}(\mathcal{I}) = \min\{|\mathcal{A}|\ :\ \mathcal{A}\subseteq \mathcal{I}\ \wedge\ (\forall I\in \mathcal{I})(\exists A\in \mathcal{A})\ I\subseteq A\}$
Is known many things when $\mathcal{I}$ is the Meager Ideal ($\mathcal{K}$) or the Null Ideal ($\mathcal{L}$) (for example, the Cichoń's diagram), but I ask about the Nowhere Dense Ideal: $\mathrm{add}$ and $\mathrm{non}$ are $\omega$ (by the rationals numbers), $\mathrm{cov}$ its equal to $\mathrm{cov}(\mathcal{K})$ because every meager set its cover by $\omega$ nowhere dense sets, but what about $\mathrm{cof}$ of nowhere dense ideal? I feel that its $\mathfrak{c}$ (the cardinality of $\mathbb{R}$) but I can't prove or disprove it.
Any help or refenrence? Thanks a lot!