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Theorems · Definition · category theory

QuadraticModuleCat.Hom.toIsometry

{R : Type u} → [inst : CommRing R] → {X Y : QuadraticModuleCat R} → X.Hom Y → X.form →qᵢ Y.form

Turn a morphism in QuadraticModuleCat back into a Isometry.

Defined in
Mathlib.LinearAlgebra.QuadraticForm.QuadraticModuleCat
Cited by
18 results in Mathlib
Foundations
Depth 50 from the axioms · uses propext, Quot.sound
Assumes
CommRing

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.Iso.toIsometryEquiv · cited by 5Iso.toIsometryEquivQuadraticModuleCat.cliffordAlgebra · cited by 2QuadraticModuleCat.cliffo…QuadraticModuleCat.hom_ext · cited by 1QuadraticModuleCat.hom_extQuadraticModuleCat.cliffordAlgebra_map · cited by 0QuadraticModuleCat.cliffo…QuadraticModuleCat.forget₂_map · cited by 0QuadraticModuleCat.forget…QuadraticModuleCat.Hom.toIsometry_injective · cited by 0Hom.toIsometry_injectiveQuadraticModuleCat.hom_ext_iff · cited by 0QuadraticModuleCat.hom_ex…QuadraticModuleCat.hom_hom_associator · cited by 0QuadraticModuleCat.hom_ho…QuadraticModuleCat.hom_inv_associator · cited by 0QuadraticModuleCat.hom_in…CategoryTheory.Iso.toIsometryEquiv_invFun · cited by 0Iso.toIsometryEquiv_invFunCategoryTheory.Iso.toIsometryEquiv_toFun · cited by 0Iso.toIsometryEquiv_toFunQuadraticModuleCat.toIsometry_comp · cited by 0QuadraticModuleCat.toIsom…QuadraticModuleCat.toIsometry_hom_leftUnitor · cited by 0QuadraticModuleCat.toIsom…QuadraticModuleCat.toIsometry_hom_rightUnitor · cited by 0QuadraticModuleCat.toIsom…QuadraticModuleCat.toIsometry_id · cited by 0QuadraticModuleCat.toIsom…CommRing · cited by 17173CommRingCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homModuleCat.carrier · cited by 997ModuleCat.carrierQuadraticMap.Isometry · cited by 69QuadraticMap.IsometryQuadraticModuleCat · cited by 40QuadraticModuleCatQuadraticModuleCat.toModuleCat · cited by 32QuadraticModuleCat.toModu…QuadraticModuleCat.form · cited by 30QuadraticModuleCat.formQuadraticModuleCat.Hom · cited by 6QuadraticModuleCat.HomHom.toIsometryCITED BYCITES

Cites8

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Cited by20

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