A reference for an explicit statement of the Galois correspondence in a Galois category

Question

The definition of a Galois category was cooked up intentionally to create the general setting where Galois correspondences appear. There are plenty of the resources (e.g. here and here) that go into detail about Galois categories, their properties, etc.

However, I have not been able to find a source that explicitly states and proves the Galois correspondence in this general setting. Is there a resource that does this?

score 3 · Accepted Answer · answered Apr 29 '19 at 07:04

3

Anna Cadoret's article Galois Categories in Arithmetic and Geometry around Galois Theory.

answered Apr 29 '19 at 07:04

Alex Youcis

56,595

Are you referring to her Proposition 3.5 on page 184 (pg. 14 on PDF)? – Santana Afton Apr 29 '19 at 07:25
@SantanaAfton Yes. Is this not what you wanted? – Alex Youcis Apr 29 '19 at 07:27
I think this is perfect. I’m still wrapping my head around the notation, but this looks like what I was after. Thanks so much! – Santana Afton Apr 29 '19 at 07:28
@SantanaAfton No problem. Good luck :) – Alex Youcis Apr 29 '19 at 07:28

A reference for an explicit statement of the Galois correspondence in a Galois category

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