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I would like to find explicit definitions of pseudo, or even lax, algebras for a 2-monad, and their lax morphisms, with all the coherence diagrams included.

Alternatively, coherent lax algebras for an operad would also be welcome.

What would be a reference?

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The original reference is Marta C. Bunge, "Coherent extensions and relational algebras", Trans. Amer. Math. Soc. 197 (1974), pp. 355-390.

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