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












4












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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?






algebraic-geometry reference-request algebraic-topology category-theory galois-connections







share|cite|improve this question









$endgroup$

















    4












    $begingroup$


    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?






    algebraic-geometry reference-request algebraic-topology category-theory galois-connections







    share|cite|improve this question









    $endgroup$















      4












      4








      4





      $begingroup$


      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?






      algebraic-geometry reference-request algebraic-topology category-theory galois-connections







      share|cite|improve this question









      $endgroup$




      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?






      algebraic-geometry reference-request algebraic-topology category-theory galois-connections




      algebraic-geometry reference-request algebraic-topology category-theory galois-connections






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked 3 hours ago









      Santana AftonSantana Afton

      3,3372830




      3,3372830






















          1 Answer
          1






          active

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          3












          $begingroup$

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






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            Are you referring to her Proposition 3.5 on page 184 (pg. 14 on PDF)?
            $endgroup$
            – Santana Afton
            2 hours ago












          • $begingroup$
            @SantanaAfton Yes. Is this not what you wanted?
            $endgroup$
            – Alex Youcis
            2 hours ago










          • $begingroup$
            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!
            $endgroup$
            – Santana Afton
            2 hours ago










          • $begingroup$
            @SantanaAfton No problem. Good luck :)
            $endgroup$
            – Alex Youcis
            2 hours ago












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          1 Answer
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          1 Answer
          1






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes









          3












          $begingroup$

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






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            Are you referring to her Proposition 3.5 on page 184 (pg. 14 on PDF)?
            $endgroup$
            – Santana Afton
            2 hours ago












          • $begingroup$
            @SantanaAfton Yes. Is this not what you wanted?
            $endgroup$
            – Alex Youcis
            2 hours ago










          • $begingroup$
            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!
            $endgroup$
            – Santana Afton
            2 hours ago










          • $begingroup$
            @SantanaAfton No problem. Good luck :)
            $endgroup$
            – Alex Youcis
            2 hours ago
















          3












          $begingroup$

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






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            Are you referring to her Proposition 3.5 on page 184 (pg. 14 on PDF)?
            $endgroup$
            – Santana Afton
            2 hours ago












          • $begingroup$
            @SantanaAfton Yes. Is this not what you wanted?
            $endgroup$
            – Alex Youcis
            2 hours ago










          • $begingroup$
            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!
            $endgroup$
            – Santana Afton
            2 hours ago










          • $begingroup$
            @SantanaAfton No problem. Good luck :)
            $endgroup$
            – Alex Youcis
            2 hours ago














          3












          3








          3





          $begingroup$

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






          share|cite|improve this answer









          $endgroup$



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







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered 3 hours ago









          Alex YoucisAlex Youcis

          37.1k775115




          37.1k775115












          • $begingroup$
            Are you referring to her Proposition 3.5 on page 184 (pg. 14 on PDF)?
            $endgroup$
            – Santana Afton
            2 hours ago












          • $begingroup$
            @SantanaAfton Yes. Is this not what you wanted?
            $endgroup$
            – Alex Youcis
            2 hours ago










          • $begingroup$
            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!
            $endgroup$
            – Santana Afton
            2 hours ago










          • $begingroup$
            @SantanaAfton No problem. Good luck :)
            $endgroup$
            – Alex Youcis
            2 hours ago


















          • $begingroup$
            Are you referring to her Proposition 3.5 on page 184 (pg. 14 on PDF)?
            $endgroup$
            – Santana Afton
            2 hours ago












          • $begingroup$
            @SantanaAfton Yes. Is this not what you wanted?
            $endgroup$
            – Alex Youcis
            2 hours ago










          • $begingroup$
            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!
            $endgroup$
            – Santana Afton
            2 hours ago










          • $begingroup$
            @SantanaAfton No problem. Good luck :)
            $endgroup$
            – Alex Youcis
            2 hours ago
















          $begingroup$
          Are you referring to her Proposition 3.5 on page 184 (pg. 14 on PDF)?
          $endgroup$
          – Santana Afton
          2 hours ago






          $begingroup$
          Are you referring to her Proposition 3.5 on page 184 (pg. 14 on PDF)?
          $endgroup$
          – Santana Afton
          2 hours ago














          $begingroup$
          @SantanaAfton Yes. Is this not what you wanted?
          $endgroup$
          – Alex Youcis
          2 hours ago




          $begingroup$
          @SantanaAfton Yes. Is this not what you wanted?
          $endgroup$
          – Alex Youcis
          2 hours ago












          $begingroup$
          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!
          $endgroup$
          – Santana Afton
          2 hours ago




          $begingroup$
          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!
          $endgroup$
          – Santana Afton
          2 hours ago












          $begingroup$
          @SantanaAfton No problem. Good luck :)
          $endgroup$
          – Alex Youcis
          2 hours ago




          $begingroup$
          @SantanaAfton No problem. Good luck :)
          $endgroup$
          – Alex Youcis
          2 hours ago


















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