Topologization and Functional Analytification III

In this paper, we continue our study on the topologization and functional analytification in $\mathrm{\infty }$-categorical and homotopical analytic geometry. As in our previous articles on the $\mathrm{\infty }$-categorical extensions of certain analytic and topological contexts, we discuss the corresponding prismatic cohomological constructions after Bhatt-Lurie, Bhatt-Scholze and Drinfeld, and the corresponding Robba stacks and sheaves after Kedlaya-Liu.