Remarks on Units of Skew Monoidal Categories

TL;DR

This paper proves the uniqueness of units in skew monoidal categories and explores the implications of additional unit structures, clarifying foundational aspects of skew monoidal category theory.

Contribution

It establishes the uniqueness of units up to isomorphism in skew monoidal categories and analyzes the independence of axioms and the effects of extra unit structures.

Findings

Units in skew monoidal categories are unique up to a unique isomorphism.

The independence of certain axioms in skew monoidal categories is demonstrated.

Additional structures on units can provide benefits in the theory.

Abstract

This article shows that the units of a skew monoidal category are unique up to a unique isomorphism, and internalises this fact to skew monoidales. Some benefits of certain extra structure on the unit maps are also discussed before the axioms of a skew monoidal category are shown to be independent.