Pita factorisation in operadic categories

Michael Batanin, Joachim Kock, Mark Weber

In strictly factorisable operadic categories, every morphism $f$ factors uniquely as $f={\eta }_f\circ {\pi }_f$ where ${\eta }_f$ is order-preserving and ${\pi }_f$ is a quasibijection that is order-p…