From coherent structures to universal properties (Q5954120)

For categorical structure (such as coproduct) defined by universal properties, the coherence requirements are essentially automatic. One of the motivations for considering multicategories was to give abstract tensor products a universal flavour and so sweep aside coherence questions. The present paper puts this in a general setting in terms of 2-monads on 2-categories and provides a general coherence theorem. Apart from monoidal categories, the theorem is applied to internal categories, monoidal globular categories, and category-valued pseudo-functors.