Has the category of Boolean algebras all small limits? If so, is there a general result for showing that a category of algebras is complete such that one can show the category of Bolean algebras is complete as a particular case?
2026-05-05 09:44:30.1777974270
Completeness of the category of boolean algebras
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Yes, all categories that are monadic over $\mathbf{Set}$ are complete, because $\mathbf{Set}$ is.
More generally, the Eilenberg-Moore category of algebras for a monad on a category $\mathcal{C}$ has all limits that exist in $\mathcal{C}$.