Theorems · Definition · category theory
QuadraticModuleCat.Hom.toIsometry
{R : Type u} → [inst : CommRing R] → {X Y : QuadraticModuleCat R} → X.Hom Y → X.form →qᵢ Y.formTurn a morphism in QuadraticModuleCat back into a Isometry.
- 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- ModuleCat.carrierstatement · cited by 997
- QuadraticMap.Isometrystatement · cited by 69
- QuadraticModuleCatstatement and proof · cited by 40
- QuadraticModuleCat.toModuleCatstatement · cited by 32
- QuadraticModuleCat.formstatement · cited by 30
- QuadraticModuleCat.Homstatement and proof · cited by 6
Cited by20
Results whose statement or proof uses this declaration.
- CategoryTheory.Iso.toIsometryEquivproof · cited by 5
- QuadraticModuleCat.cliffordAlgebraproof · cited by 2
- QuadraticModuleCat.hom_extstatement and proof · cited by 1
- QuadraticModuleCat.cliffordAlgebra_mapstatement · cited by 0
- QuadraticModuleCat.forget₂_mapstatement · cited by 0
- QuadraticModuleCat.Hom.toIsometry_injectivestatement and proof · cited by 0
- QuadraticModuleCat.hom_ext_iffstatement and proof · cited by 0
- QuadraticModuleCat.hom_hom_associatorstatement · cited by 0
- QuadraticModuleCat.hom_inv_associatorstatement · cited by 0
- CategoryTheory.Iso.toIsometryEquiv_invFunstatement · cited by 0
- CategoryTheory.Iso.toIsometryEquiv_toFunstatement · cited by 0
- QuadraticModuleCat.toIsometry_compstatement · cited by 0