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1982•Bulletin of the Australian Mathematical SocietyOpen access

Serre classes for toposes

Murray Adelman, Peter Johnstone

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Abstract

We prove first that a logical fraction functor from a topos to a topos must be a filter-power functor, then we prove that such functors can have adjoints only when the filter is principal. Finally we refine this so that we are able to prove that the filter-power of a Grothendieck topos is Grothendieck if and only if the filter is principal.

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What this paper is about

We prove first that a logical fraction functor from a topos to a topos must be a filter-power functor, then we prove that such functors can have adjoints only when the filter is principal. Finally we refine this so that we are able to prove that the filter-power of a Grothendieck topos is Grothendieck if and only if the filter is principal.

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Available abstract

We prove first that a logical fraction functor from a topos to a topos must be a filter-power functor, then we prove that such functors can have adjoints only when the filter is principal. Finally we refine this so that we are able to prove that the filter-power of a Grothendieck topos is Grothendieck if and only if the filter is principal.

Key concepts: Topos theory, Mathematics, Functor, Filter (signal processing), Pure mathematics, Principal (computer security), Computer science, Literature

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