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Is there a monoidal structure on the category of compact Hausdorff totally disconnected topological spaces (i.e. Stone spaces)?

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Yes, the product of two Stone spaces is again a Stone space, and places a monoidal structure on the category of Stone spaces.

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  • $\begingroup$ Oh, thanks. (You are saying that it is a "cartesian" monoidal category then, right?) $\endgroup$ – GDS221 Apr 18 '16 at 15:14
  • $\begingroup$ Yes, if the monoid product is given by the ordinary product then it is called a cartesian monoidal category. $\endgroup$ – silvascientist Apr 18 '16 at 15:16

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