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Representing Geometric Morphisms Using Power Locale Monads

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Abstract

It is shown that geometric morphisms between elementary toposes can be represented as adjunctions between the corresponding categories of locales. The adjunctions are characterized as those that preserve the order enrichment, commute with the double power locale monad and whose right adjoints preserve finite coproduct. They are also characterized as those adjunctions that preserve the order enrichment and commute with both the lower and the upper power locale monads.

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  1. 8 Aylesbury Road, Tring, Hertfordshire, HP23 4DJ, UK

    Christopher F. Townsend

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  1. Christopher F. Townsend
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Correspondence to Christopher F. Townsend.

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Townsend, C.F. Representing Geometric Morphisms Using Power Locale Monads. Appl Categor Struct 21, 15–47 (2013). https://doi.org/10.1007/s10485-011-9258-z

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  • DOI: https://doi.org/10.1007/s10485-011-9258-z

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