Let $X$ be an affinoid variety over a discretely valued non-archimedean field $k$ with valuation ring $\mathcal{R}$. Fix a uniformizer $\omega$. On the section 3.2 of the paper <https://arxiv.org/abs/1501.02215> it is stated that, for every flat $O(X)^{\circ}$-module $Q$, the functor
$$A\mapsto \widehat{A\otimes\_{O(X)^{\circ}}Q}\otimes\_{\mathcal{R}}k$$
where the completion is with respect to the $\omega$-adic topology, is left exact. Showing this would involve showing that the kernel of the compled tensor is torsion, however, I do not understand why this is the case.



On the exactness of some completed tensor products
This proposition has been removed from the paper in the published paper, available in the author's webpage.


