Isbell conjugacy and the reflexive completion

Tom Avery, Tom Leinster

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

The reflexive completion of a category consists of the Set-valued functors on it that are canonically isomorphic to their double conjugate. After reviewing both this construction and Isbell conjugacy itself, we give new examples and revisit Isbell's main results from 1960 in a modern categorical context. We establish the sense in which reflexive completion is functorial, and find conditions under which two categories have equivalent reflexive completions. We describe the relationship between the reflexive and Cauchy completions, determine exactly which limits and colimits exist in an arbitrary reflexive completion, and make precise the sense in which the reflexive completion of a category is the intersection of the categories of covariant and contravariant functors on it.
Original languageEnglish
Pages (from-to)306-347
Number of pages41
JournalTheory and Applications of Categories
Volume36
Issue number12
Publication statusPublished - 1 Jun 2021

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