Skew monoidal categories and skew multicategories

TL;DR

This paper establishes a precise correspondence between skew monoidal categories and a new class of generalized multicategories called skew multicategories, which naturally occur in mathematical contexts.

Contribution

It introduces skew multicategories and proves a perfect correspondence with skew monoidal categories, expanding the understanding of their structural relationship.

Findings

Skew multicategories generalize multicategories in a natural way.

A bijective correspondence between skew monoidal categories and skew multicategories is demonstrated.

The framework applies to various mathematical structures in nature.

Abstract

We describe a perfect correspondence between skew monoidal categories and certain generalised multicategories, called skew multicategories, that arise in nature.