Is the unit compact in a closed monoidal (co)complete category? Let $\mathcal{M}$ be a complete and cocomplete closed symmetric monoidal category, with unit $I.$

Does the functor $\text{Hom}_{\mathcal{M}}(I,-)$ always preserve filtered colimits?

A reference or a proof is the same for me. I believe this should be true as it's true in many examples such as $\mathbf{Sets},$ categories of modules, presheaf toposes etc.
 A: It's not even true for all presheaf toposes.
Let $I$ be a set.
The category $\textbf{Set}^I$ is a presheaf topos, and in particular, complete and cocomplete and cartesian closed.
The terminal object $1$ is not, in general, finitely presentable.
Indeed, a general object $X$ in $\textbf{Set}^I$ is just an $I$-indexed family of sets, and the set of morphisms $1 \to X$ is in natural bijection with $\prod_{i \in I} X_i$.
Proposition.
The functor $X \mapsto \prod_{i \in I} X_i$ preserves filtered colimits if and only if $I$ is a finite set.
Proof.
The "if" direction is well known.
For the "only if" direction, observe that $X \cong \varinjlim_{J \in \mathscr{P}_\textrm{f} (I)} X_{(J)}$, where $\mathscr{P}_\textrm{f} (I)$ is the set of finite subsets of $I$ and $(X_{(J)})_i = X_i$ if $i \in J$ and $(X_{(J)})_i = \emptyset$ if $i \notin J$.
If $I$ is infinite, then $\prod_{i \in I} (X_{(J)})_i$ is always empty, hence $\varinjlim_J \prod_{i \in I} (X_{(J)})_i$ is also empty.
But $\prod_{i \in I} X_i$ may be non-empty.
So $X \mapsto \prod_{i \in I} X_i$ does not preserve filtered colimits if $I$ is infinite.　◼
