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# Units of skew monoidal categories and skew monoidales in Span

thesis
posted on 28.03.2022, 11:19 by Jim Andrianopoulos
This thesis is about skew monoidal categories and consists of two relatively independent chapters, the first of which 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. We include some remarks on the unit conditions for a monoidal functor between skew monoidal categories that generalises the earlier uniqueness result. In the second, an interesting characterisation of a skew monoidale in the monoidal bicategory Span is given, generalising the case where the unit of the skew monoidale is of a certain restricted form, along with an example. Finally in an appendix, we show that the five axioms of a skew monoidal category are independent.

## History

1. Introduction -- 2. Skew monoidal categories -- 3. Skew monoidales in Span -- Appendix A. Independence of the axioms -- Appendix B. Gray monoids.

## Notes

"This thesis is presented for the degree of Master of Philosophy, Department of Mathematics". Bibliography: pages 57-59 "1 May 2015".

## Awarding Institution

Macquarie University

Thesis MPhil

## Degree

MPhil, Macquarie University, Faculty of Science and Engineering, Department of Mathematics

## Department, Centre or School

Department of Mathematics

2015

Stephen Lack

English

## Extent

1 online resource (iv, 59 pages)

## Former Identifiers

mq:44191 http://hdl.handle.net/1959.14/1067106

## Exports

figshare. credit for all your research.