TL;DR
This paper provides an explicit description of the free skew monoidal category generated by any category, enhancing understanding of skew monoidal structures and their relationships with operads.
Contribution
It offers a detailed, explicit construction of the free skew monoidal category and explores adjunctions with simpler operads, advancing the theoretical framework.
Findings
Explicit description of the free skew monoidal category
Identification of skew monoidal categories with colax L-algebras
Connections between operads for skew monoidal categories and simpler operads
Abstract
In the paper "Triangulations, orientals, and skew monoidal categories", the free monoidal category Fsk on a single generating object was described. We sharpen this by giving a completely explicit description of Fsk, and so of the free skew monoidal category on any category. As an application we describe adjunctions between the operad for skew monoidal categories and various simpler operads. For a particular such operad L, we identify skew monoidal categories with certain colax L-algebras.
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