In algebra, given a 2-monad T in a 2-category, a pseudoalgebra for T is a 2-category-version of algebra for T, that satisfies the laws up to coherent isomorphisms.
See also Operad
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Further reading
External links https://ncatlab.org/nlab/show/pseudoalgebra+for+a+2-monad https://golem.ph.utexas.edu/category/2014/06/codescent_objects_and_coherenc.html