Coherence for skew monoidal categories, revisited

Steve Lack – 8 March 2017

After recalling Kelly's notion of club over N, and its correspondence with plane Cat-operads, I talked about the club/operad for skew monoidal categories, which was constructed in the Lack-Street paper Coherence for skew monoidal categories [Advances, 2014]. This described the free skew monoidal category generated by an object, and proved that it had a faithful structure-preserving map to the (skew monoidal) category of non-empty finite ordinals and order-and-bottom-preserving maps.

In the paper, the image of this functor was not described as explicitly as one might hope for. In the talk, I described how to make this completely explicit.

This is joint work with John Bourke, motivated by our on-going investigations into a multicategorical approach to skew monoidal categories