??so what's an "idempotent monoid" ?? ??monoid x where ... ???multiplication is isomorphism from x tensor x to x ... ???or something ???... ???... and so forth ...
??walking idempotent monoid ... ??? ... and so forth ... ???....
??idempotent monoids in monoidal category of abelian groups under tensor product, for example ... ??being a module of such a ring as a mere property ... ???or something?? ...
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