Adjoints, multi-adjoints, pluri-adjoints
type: Item
instance of: scholarly article
title: Adjoints, multi-adjoints, pluri-adjoints
zbMATH Open document ID: 0835.18002
author: Alexandru Solian
author: T. M. Viswanathan
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 1996-04-16T00:00:00Z
full work available at URL: https://eudml.org/doc/225383
review text: Let \((G_p: {\mathcal A}_p\to {\mathcal X})_{p\in P}\) be a small family of functors having left adjoints, between small categories. If \({\mathcal A}\) is the coproduct of \(({\mathcal A}_p )_{p\in P}\) in \({\mathcal C}at\), the functor \(G: {\mathcal A}\to {\mathcal X}\) defined by \((G_p )_{p\in P}\) is proved to have a left multiadjoint in the sense of the reviewer. With some additional assumptions on \({\mathcal A}_p\) and \({\mathcal X}\), the authors build up a small category \(\overline {\mathcal A}\) and a functor \(\overline {G}: \overline {\mathcal A}\to {\mathcal X}\) which has a left pluriadjoint in the sense of the authors. These constructions show how the transitions from adjoint to multiadjoint, and from multiadjoint to pluriadjoint can be performed.
Mathematics Subject Classification ID: 18A40
Mathematics Subject Classification ID: 18A35
zbMATH DE Number: 817245
zbMATH Keywords: adjoints
zbMATH Keywords: small categories
zbMATH Keywords: multiadjoint
zbMATH Keywords: pluriadjoint
reviewed by: Yves Diers
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 817245