Transport along a cofibration is converted, by a change of 2-monads, into the cocartesian–vertical factorization of arrows in the total category.
Factorization systems as Eilenberg–Moore algebras.J
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From Grothendieck cofibrations to factorization systems: a formal 2-monadic account
Transport along a cofibration is converted, by a change of 2-monads, into the cocartesian–vertical factorization of arrows in the total category.