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Theorems · Definition · group theory

Function.Surjective.torsor

{G : Type u_1} →
  {P : Type u_2} →
    {Q : Type u_3} →
      [inst : Group G] →
        [inst_1 : Torsor G P] →
          [inst_2 : SMul G Q] →
            [inst_3 : SDiv G Q] →
              (f : P → Q) →
                Function.Surjective f →
                  (∀ (c : G) (x : P), f (c • x) = c • f x) → (∀ (x y : P), x /ₛ y = f x /ₛ f y) → Torsor G Q

Pushforward of a torsor along a surjective map.

Defined in
Mathlib.Algebra.Torsor.Basic
Cited by
0 results in Mathlib
Foundations
Depth 11 from the axioms · uses propext, Quot.sound
Assumes
GroupTorsorSMulSDiv
Mathlib docsSourceLoogleLeanSearch

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Group · cited by 6238GroupMulAction · cited by 1294MulActionSDiv.sdiv · cited by 79SDiv.sdivTorsor · cited by 65TorsorSDiv · cited by 27SDivFunction.Surjective.mulAction · cited by 0Surjective.mulActionSurjective.torsorCITED BYCITES

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