Tate modules as condensed modules

We prove that the category of countable Tate modules over an arbitrary discrete ring embeds fully faithfully into that of condensed modules. If the base ring is of finite type, we characterize the essential image as generated by the free module of infinite countable rank under direct sums, duals and retracts. In the (Formula presented.) -categorical context, under the same assumption on the base ring, we establish a fully faithful embedding of the (Formula presented.) -category of countable Tate objects in perfect complexes, with uniformly bounded tor-amplitude, into the derived (Formula presented.) -category of condensed modules. The boundedness assumption is necessary to ensure fullness, as we prove via an explicit counterexample in the unbounded case.