= Creation of limits up to isomorphism
An equivalence-invariant lifting property permits the underlying cone of the lift to be identified with the chosen cone by an isomorphism, rather than requiring literal equality. Lifts are unique up to a unique isomorphism compatible with that identification. A <monadic adjunction> defined by equivalence of its comparison functor has this property by <monad algebra forgetful functor creates limits>. Literal creation follows if the comparison is an isomorphism over the base, or suitable strict transport of objects is part of the convention. An equivalence alone does not guarantee a literally prescribed underlying object lies in the image.
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