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Enriched regular theories

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posted on 29.03.2022, 02:08 authored by Giacomo Tendas
Regular and exact categories were first introduced by Michael Barr in 1971; since then, the theory has developed and found many applications in algebra, geometry, and logic. In particular, a small regular category determines a certain theory, in the sense of logic, whose models are the regular functors into Set. In 1986 Barr showed that each small and regular category can be embedded in a particular category of presheaves; then in 1990 Makkai gave a simple explicit characterization of the essential image of the embedding, in the case where the original regular category is moreover exact. More recently Prest and Rajani, in the additive context, and Kuber and Rosicky, in the ordinary one, described a duality which connects an exact category with its (definable) category of models. Considering a suitable base for enrichment, we define an enriched notion of regularity and exactness, and prove a corresponding version of the theorems of Barr, of Makkai, and of Prest-Rajani/Kuber-Rosicky.


Table of Contents

Introduction -- 1. Background -- 2. Bases for enrichment -- 3. Regular and exact V-categories -- 4. Definable V-categories -- 5. Future directions -- Bibliography.


Empirical thesis. Bibliography: pages 51-52

Awarding Institution

Macquarie University

Degree Type

Thesis MRes


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

Department, Centre or School

Department of Mathematics and Statistics

Year of Award


Principal Supervisor

Stephen Lack


Copyright Giacomo Tendas 2019. Copyright disclaimer: http://mq.edu.au/library/copyright




1 online resource (i, 52 pages)

Former Identifiers

mq:71058 http://hdl.handle.net/1959.14/1270426