Theorems · Definition · commutative algebra

Ideal.Quotient.stabilizerHomSurjectiveAuxFunctor

{A : Type u_1} →
  {B : Type u_2} →
    [inst : CommRing A] →
      [inst_1 : CommRing B] →
        [inst_2 : Algebra A B] →
          {G : Type u} →
            [inst_3 : Group G] →
              [inst_4 : MulSemiringAction G B] →
                [SMulCommClass G A B] →
                  [inst_6 : TopologicalSpace G] →
                    (P : Ideal A) →
                      (Q : Ideal B) →
                        [inst_7 : Q.LiesOver P] →
                          ((B ⧸ Q) ≃ₐ[A ⧸ P] B ⧸ Q) → CategoryTheory.Functor (OpenNormalSubgroup G) (Type u)

(Implementation) The functor taking an open normal subgroup N ≤ G to the set of lifts of σ in G ⧸ N. We will show that its inverse limit is nonempty to conclude that there exists a lift in G.

Defined in

Mathlib.RingTheory.Invariant.Profinite

Cited by

1 results in Mathlib

Foundations

Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraGroupMulSemiringActionSMulCommClassTopologicalSpaceIdeal.LiesOver