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Questions taking place in the category of locales, which is given by the opposite of the category of frames. Also appropriate for questions about pointless topology.
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How algebraic can the dual of a topological category be?
One of the nice aspects of the category of locales, $\mathrm{Loc}$, is that its dual (the category of frames) is monadic (over $\mathrm{Set}$) and therefore algebraic in this sense. … category $(A,G)$ with $A^{\mathrm{op}}$ monadic or algebraic such that any of the common categories of spaces (e.g., compact Hausdorff spaces, compactly generated weak Hausdorff spaces, topological spaces, locales …