Cartesian monads on toposes
type: Item
instance of: scholarly article
title: Cartesian monads on toposes
zbMATH Open document ID: 0881.18001
DOI: 10.1016/S0022-4049(96)00165-X
published in: Journal of Pure and Applied Algebra
publication date: 1998-01-18T00:00:00Z
review text: A geometric morphism between toposes, being an adjoint pair of left exact functors, induces a left exact monad on the codomain. The author addresses the question whether any left exact monad on a topos arises this way. The answer is positive provided the topos is Boolean. The proof technique is: use the existing theory of strong and indexed monads to reduce the question to the case where the topos is the category of \({\mathcal S}ets\). Here, left exact monads are shown to correspond bijectively to strongly zero dimensional locales, and these give rise to the desired geometric morphisms.
reviewed by: Anders Kock
Mathematics Subject Classification ID: 18B25
Mathematics Subject Classification ID: 08B99
Mathematics Subject Classification ID: 18C15
Mathematics Subject Classification ID: 06E99
zbMATH DE Number: 1004400
zbMATH Keywords: monad
zbMATH Keywords: topos
zbMATH Keywords: geometric morphism
zbMATH Keywords: zero-dimensional locale
author: Peter Johnstone
MaRDI profile type: Publication
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full work available at URL: s0022-4049(96)00165-x
OpenAlex ID: W2151448345
description: scientific article; zbMATH DE number 1004400