Theorems · Theorem · category theory

ModuleCat.homEquiv_extendScalarsId

∀ {R : Type u₁} [inst : CommRing R] (M : ModuleCat R),
  ((ModuleCat.extendRestrictScalarsAdj (RingHom.id R)).homEquiv M ((CategoryTheory.Functor.id (ModuleCat R)).obj M))
      ((ModuleCat.extendScalarsId R).hom.app M) =
    (ModuleCat.restrictScalarsId R).inv.app M

Defined in: Mathlib.Algebra.Category.ModuleCat.ChangeOfRings
Cited by: 1 results in Mathlib
Foundations: Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing

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Cites28

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Quiver.Homstatement · cited by 32,603
CategoryTheory.Functor.objstatement and proof · cited by 19,642
RingHom.idstatement and proof · cited by 18,349
CommRingstatement and proof · cited by 17,173
CategoryTheory.Functorstatement · cited by 16,252
Equivstatement · cited by 8,337
CategoryTheory.Iso.homstatement and proof · cited by 7,684
CategoryTheory.NatTrans.appstatement and proof · cited by 7,406
CategoryTheory.Iso.invstatement and proof · cited by 6,514
CategoryTheory.ConcreteCategory.homproof · cited by 4,022
CategoryTheory.Functor.idstatement and proof · cited by 3,333

Cited by1

Results whose statement or proof uses this declaration.

ModuleCat.extendScalarsId_hom_app_one_tmulproof · cited by 2