Diads and their application to topoi
type: Item
instance of: scholarly article
title: Diads and their application to topoi
zbMATH Open document ID: 1201.18002
author: Toby Kenney
published in: Applied Categorical Structures
publication date: 2010-01-15T00:00:00Z
review text: As a common generalisation of monads and comonads the author introduces the concept of a diad. He demonstrates that many of the constructions performable for monads resp. comonads can be extended to diads. In particular, for diads so called dialgebras can be constructed as common generalisation of algebras of a monad resp. coalgebras of a comonad. Main result: the category of dialgebras for a finite--limit preserving left diad on a topos is again a topos.
reviewed by: Horst Herrlich
Mathematics Subject Classification ID: 18B25
Mathematics Subject Classification ID: 18C15
Mathematics Subject Classification ID: 18A35
zbMATH DE Number: 5659531
zbMATH Keywords: topos
zbMATH Keywords: (co)monad
zbMATH Keywords: diad
zbMATH Keywords: (co)algebra
zbMATH Keywords: dialgebra
MaRDI profile type: Publication
full work available at URL: s10485-008-9156-1
OpenAlex ID: W2016959028
cites work: Q4783274
cites work: The general theory of diads
cites work: Q4380421
cites work: Idempotents in bicategories
cites work: Relations binaires, fermetures, correspondances de Galois
cites work: Q5796583
DOI: 10.1007/S10485-008-9156-1
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description: scientific article; zbMATH DE number 5659531