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Local reflections between relations, spans and polynomials

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posted on 2022-03-28, 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.


Table of Contents

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


Bibliography: pages [61]-62 Theoretical thesis.

Awarding Institution

Macquarie University

Degree Type

Thesis MRes


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

Department, Centre or School

Department of Mathematics

Year of Award


Principal Supervisor

Richard Garner


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




1 online resource (x, 62 pages)

Former Identifiers

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