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So this “successor” monad is clearly an instance for the category of sets of the maybe monad. Is the successor monad truly specific to Set, though, or is it another name for maybe, and this page just happens to be interested in the Set case?
I figure some link between them should be put in, but I’m not sure what to say. I’ve put a link on maybe monad.
I can’t think of a reason why it wasn’t called “maybe”, unless there’s some concept with an attitude thing happening that I don’t know about.
Note: the way I use “décalage comonad”, it’s a comonad on simplicial objects, rather than on the opposite of the simplex category.
I copied across the information about the simplex category to maybe monad. So should we just redirect this page there?
Yeah, I think it’s probably best to merge these pages. The bit about material set theory could go in an unobtrusive remark, if we want to keep it.
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