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Characterising asymmetric lenses using internal categories

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thesis
posted on 28.03.2022, 11:34 by Bryce Clarke
Asymmetric lenses were originally defined in Computer Science as a solution to the view update problem, and are mathematically well understood as a generalisation of split opfibrations. In this thesis, we utilise internal category theory to unify three kinds of asymmetric lens — set-based, c-lenses, and d-lenses — through the construction of an internal category of view updates produced using the well-known lens laws. We show that this category forms the head of a span of internal functors, which induces a commutative triangle with the Get of a lens. The composition of these commuting triangles is used to characterise the three categories Lens, Clens, and Dlens.

History

Table of Contents

1. Introduction -- 2. Background -- 3. Internal characterisation of set-based lenses -- 4. Internal characterisation of c-lenses -- 5. Internal characterisation of d-lenses -- 6. Conclusion -- References.

Notes

"Centre of Australian Category Theory (CoACT), Department of Computing" -- title page. Bibliography: pages 49-50 Empirical thesis.

Awarding Institution

Macquarie University

Degree Type

Thesis MRes

Degree

MRes, Macquarie University, Faculty of Science and Engineering, Department of Computing

Department, Centre or School

Department of Computing

Year of Award

2018

Principal Supervisor

Michael Johnson

Rights

Copyright Bryce Clarke 2018. Copyright disclaimer: http://mq.edu.au/library/copyright

Language

English

Extent

1 online resource (x, 50 pages)

Former Identifiers

mq:70915 http://hdl.handle.net/1959.14/1268984