Added a note that this is different from the usual definition of an idempotent monoid in algebra.
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]]>It’s reasonable to redirect idempotent semigroup to this page, even if it’s mainly about idempotent monoids. I don’t see a problem with terminology like semigroupal category, considering we already have magmoidal category and the like.
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]]>I agree “idempotent semigroup (object)” seems most suitable when associativity is present. I think “object” can be omitted in this instance, as there ought to be no confusion.
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]]>Also, should idempotent monoids have a unit?
When there is no unit, surely the appropriate terminology is “idempotent magma”.
]]>Nice!
I have added hyperlinks to more of the technical term appearing (such Spectra).
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