Theorems · Definition · category theory
ModuleCat.extendScalarsId
(R : Type u₁) → [inst : CommRing R] → ModuleCat.extendScalars (RingHom.id R) ≅ CategoryTheory.Functor.id (ModuleCat R)
The extension of scalars by the identity of a ring is isomorphic to the identity functor.
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- RingHom.idstatement and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- CategoryTheory.Functorstatement · cited by 16,252
- CategoryTheory.Isostatement · cited by 3,963
- Equiv.symmproof · cited by 3,681
- CategoryTheory.Functor.idstatement · cited by 3,333
- ModuleCatstatement · cited by 1,429
- CategoryTheory.Iso.symmproof · cited by 993
- ModuleCat.extendScalarsstatement · cited by 39
- CategoryTheory.Adjunction.idproof · cited by 12
- ModuleCat.extendRestrictScalarsAdjproof · cited by 7
Cited by9
Results whose statement or proof uses this declaration.
- CommRingCat.moduleCatExtendScalarsPseudofunctorproof · cited by 4
- ModuleCat.extendScalarsId_hom_app_one_tmulstatement and proof · cited by 2
- ModuleCat.extendScalarsId_inv_app_applystatement · cited by 1
- ModuleCat.extendScalars_comp_idstatement and proof · cited by 1
- ModuleCat.extendScalars_id_compstatement and proof · cited by 1
- ModuleCat.homEquiv_extendScalarsIdstatement and proof · cited by 1
- CommRingCat.moduleCatExtendScalarsPseudofunctor_mapIdstatement · cited by 0
- ModuleCat.extendScalars_comp_id_assocstatement and proof · cited by 0
- ModuleCat.extendScalars_id_comp_assocstatement and proof · cited by 0