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Applied Categorical Structures

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02-08-2021

Isbell Adjunctions and Kan Adjunctions via Quantale-Enriched Two-Variable Adjunctions

Authors: Lili Shen, Xiaoye Tang

Published in: Applied Categorical Structures | Issue 2/2022

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Abstract

It is shown that every two-variable adjunction in categories enriched in a commutative quantale serves as a base for constructing Isbell adjunctions between functor categories, and Kan adjunctions are precisely Isbell adjunctions constructed from suitable associated two-variable adjunctions. Representation theorems are established for fixed points of these adjunctions.

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Strictly speaking, “fixed point” should read “pseudo-fixed point” here, since \(a\in \mathsf{Fix}(h)\) satisfies \(ha\cong a\) instead of \(ha=a\).

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Title: Isbell Adjunctions and Kan Adjunctions via Quantale-Enriched Two-Variable Adjunctions
Authors: Lili Shen
Xiaoye Tang
Publication date: 02-08-2021
Publisher: Springer Netherlands
Published in: Applied Categorical Structures / Issue 2/2022
Print ISSN: 0927-2852
Electronic ISSN: 1572-9095
DOI: https://doi.org/10.1007/s10485-021-09654-w

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