Theorems · Definition · category theory
CategoryTheory.Iso.toLinearEquiv
{R : Type u} → [inst : Ring R] → {X Y : ModuleCat R} → (X ≅ Y) → ↑X ≃ₗ[R] ↑YBuild a LinearEquiv from an isomorphism in the category ModuleCat R.
- Defined in
- Mathlib.Algebra.Category.ModuleCat.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement · cited by 18,349
- CategoryTheory.Iso.homproof · cited by 7,684
- Ringstatement and proof · cited by 7,463
- CategoryTheory.Iso.invproof · cited by 6,514
- CategoryTheory.Isostatement and proof · cited by 3,963
- LinearEquivstatement · cited by 3,317
- ModuleCatstatement and proof · cited by 1,429
- ModuleCat.carrierstatement · cited by 997
- ModuleCat.Hom.homproof · cited by 341
- LinearEquiv.ofLinearMapproof · cited by 9
Cited by9
Results whose statement or proof uses this declaration.
- FGModuleCat.isoToLinearEquivproof · cited by 3
- linearEquivIsoModuleIsoproof · cited by 2
- AlgebraicGeometry.isLocalizing_of_isIso_app_topproof · cited by 1
- linearEquivIsoModuleIso_invstatement · cited by 0
- CategoryTheory.Iso.toLinearEquiv_applystatement · cited by 0
- CategoryTheory.Iso.toLinearEquiv_symmstatement · cited by 0
- CategoryTheory.Iso.toLinearMap_toLinearEquivstatement · cited by 0
- ModuleCat.Iso.conj_eq_conjstatement · cited by 0
- ModuleCat.Iso.homCongr_eq_arrowCongrstatement · cited by 0