Post #1733536
2026-04-27 19:39 UTC
Is there a notion of surjectivity for morphisms of locales (I'm wondering this mostly with algebraic geometry in mind)?
@MartinEscardo
Replies (2)
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@jonmsterling@mathstodon.xyz 2026-04-27 19:42
@jdw @MartinEscardo Yes, a surjection is when the inverse image functor is conservative (or, equivalently, faithful). I don’t know enough, however, to comment on implications for algebraic geometry.
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@MartinEscardo@mathstodon.xyz 2026-04-27 19:55
@jdw writes "Is there a notion of surjectivity for morphisms of locales". Yes, and this t is an important notion. In fact, my colleague Steve Vickers has argued that surjectivity behaves better for locales than for topological spaces, when you work constructively. Here is one example: https://sjvickers.github.io/papersfull.html#IntervalNote But he also gave more examples in his 7WFTop talk in Venice recently.