Models of enhanced limit 2-sketches are equivalent to algebras over enhanced 2-monads, including lax morphisms, and inherit w-rigged limits.
Comparing loose bimodules and double barrels using pseudo-models of enhanced sketches
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Enhanced $2$-categories of models of sketches as enhanced $2$-categories of algebras over monads
Models of enhanced limit 2-sketches are equivalent to algebras over enhanced 2-monads, including lax morphisms, and inherit w-rigged limits.