Consider the category $\operatorname{Solid}_{\mathbf{Z}}$ of *solid* abelian groups in the sense of Clausen-Scholze. This category is a full subcategory of *condensed* abelian groups, $\operatorname{Cond}_{\mathbf{Z}}$. These are, modulo set theoretical technicalities, abelian sheaves on the site of profinite sets, with finite families of jointly surjective maps as coverings. There is a left adjoint to the inclusion, and thus one can define a tensor product by tensoring in $\operatorname{Cond}_{\mathbf{Z}}$ and then solidifying.

**Question**. Let $V$ be a pro-discrete topological abelian group. Note that $\mathbf{Z}((T))$ is solid, as it is the limit along open inclusions of pro-discrete spaces, and any map from a compact space must factor through some pro-discrete subspace. What is the solid tensor product of $V$ with $\mathbf{Z}((T))$? I presume it is $V\{T\}$, the module of two way infinite Laurent series over $V$, whose Laurent tail coefficients tend to $0$ in $V$? To prove this it would seem I need to prove that the solid tensor product commutes with certain cofiltered limits, which I have not been able to do.