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Local reflections between relations, spans and polynomials

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thesis
posted on 28.03.2022, 11:45 authored by Charles R. Walker
Given a locally cartesian closed regular category ξ we may form the bicategories of relations, spans and ploynomials. We show that for each hom-category, relations are a reflective subcategory of spans, and spans are a coreflective subcategory of ploynomials (with cartesian 2-cells). We then use these local reflections and coreflections to derive the universal property of relations from that of spans, and construct a right adjoint to the inclusion of spans into polynomials in the 2-category of bicategories, lax functors and icons. Moreover, we show that this right adjoint becomes a pseudofunctor if we restrict ourselves to polynomials for which the middle map is a monomorphism, or alternatively if we restrict ourselves to polynomials for which this map is a regular epimorphism.

History

Table of Contents

1. Introduction -- 2. Background -- 3. Local reflections -- 4. Pulling back into isomorphisms -- 5. Polynomial reflections -- 6. Future directions.

Notes

Bibliography: pages [61]-62 Theoretical thesis.

Awarding Institution

Macquarie University

Degree Type

Thesis MRes

Degree

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

Department, Centre or School

Department of Mathematics

Year of Award

2015

Principal Supervisor

Richard Garner

Rights

Copyright Charles R. Walker 2015. Copyright disclaimer: http://www.copyright.mq.edu.au

Language

English

Extent

1 online resource (x, 62 pages)

Former Identifiers

mq:44519 http://hdl.handle.net/1959.14/1069952