Extensivity relative to a bifunctor

Extensive categories capture a fundamental feature of the category of sets: their coproducts are both disjoint and universal. Two equivalent formulations of extensive categories provide two distinct perspectives on the notion. The first is as a property of functors, and the second as a property of morphisms in the category. This thesis explores both perspectives. The morphism-focused viewpoint is captured through extensive morphisms, which allow one to study extensivity in categories that are not themselves extensive. From the functorial viewpoint, we introduce near-sums, functorial replacements for coproducts in categories lacking them. Near-sums provide a natural setting for extending the theory of extensive categories, capturing key features thereof, such as disjointness and universality.

Grantor dc:publisher

Stellenbosch : Stellenbosch University

Year dc:date.issued

2026

Author dc:creator

• Theart, Emma

Advisor dc:contributor.advisor

• Hoefnagel, Michael

Language dc:language.iso

en

Repository record dc:identifier.uri

https://scholar.sun.ac.za/handle/10019.1/135773

OAI identifier oai:identifier

oai:scholar.sun.ac.za:10019.1/135773