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Wondering for the ncatlab I've encountered the following pages: one about lax-morphisms and the other about lax-algebras for $2$-monads.

For what I could get it seems that lax algebras can be characterized as lax morphisms in a category of strict algebras for a strict $2$-monad having as algebras the strict monads.

Could anyone write down more explicitly this construction or link any reference where such characterization is spelled out?

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