Theorems · Definition · category theory

QuadraticModuleCat.ofIso

{R : Type u} →
  [inst : CommRing R] →
    {X Y : Type v} →
      [inst_1 : AddCommGroup X] →
        [inst_2 : Module R X] →
          [inst_3 : AddCommGroup Y] →
            [inst_4 : Module R Y] →
              {Q₁ : QuadraticForm R X} →
                {Q₂ : QuadraticForm R Y} →
                  QuadraticMap.IsometryEquiv Q₁ Q₂ → (QuadraticModuleCat.of Q₁ ≅ QuadraticModuleCat.of Q₂)

Build an isomorphism in the category QuadraticModuleCat R from a QuadraticForm.IsometryEquiv.

Defined in

Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat

Cited by

5 results in Mathlib

Foundations

Depth 52 from the axioms · uses propext, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModule