Higher-dimensional Mac Laneʹs pentagon and Zamolodchikov equations

An important ingredient of Mac Laneʹs coherence theorem for monoidal categories is Mac Laneʹs pentagon, a diagram whose commutativity is needed so that “all diagrams commute”. This paper gives a higher-dimensional generalization of Mac Laneʹs pentagon: a 6-dimensional diagram whose commutativity is needed in order for all diagrams in somewhat weak teisi to commute.