Conditions on double categories are identified making the category of monads monadic over endomorphisms and cocomplete or locally presentable, with dual results for comonads.
A unified treatment of commuting tensor products of categories, operads, symmetric multicategories and their bimodules
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On categories of monads and comonads in double categories
Conditions on double categories are identified making the category of monads monadic over endomorphisms and cocomplete or locally presentable, with dual results for comonads.