Theorems · Definition · category theory
AlgCat.restrictScalars
{R : Type u_1} →
{S : Type u_2} →
[inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → CategoryTheory.Functor (AlgCat S) (AlgCat R)The restriction of scalars functor AlgCat S ⥤ AlgCat R induced by a ring homomorphism
R →+* S.
- Defined in
- Mathlib.Algebra.Category.AlgCat.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Quot.sound
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.
- Quiver.Homproof · cited by 32,603
- CommRingstatement and proof · cited by 17,173
- CategoryTheory.Functorstatement · cited by 16,252
- RingHomstatement and proof · cited by 10,189
- AlgHom.restrictScalarsproof · cited by 83
- AlgCatstatement and proof · cited by 75
- AlgCat.carrierproof · cited by 61
- AlgCat.Hom.homproof · cited by 27
- AlgCat.ofproof · cited by 23
- AlgCat.ofHomproof · cited by 16
Cited by13
Results whose statement or proof uses this declaration.
- AlgCat.restrictScalarsComp'statement · cited by 4
- AlgCat.restrictScalarsEquivalenceOfRingEquivproof · cited by 4
- AlgCat.restrictScalarsId'statement · cited by 4
- AlgCat.restrictScalarsComp'_hom_app_hom_applystatement · cited by 0
- AlgCat.restrictScalarsComp'_inv_app_hom_applystatement and proof · cited by 0
- AlgCat.restrictScalarsEquivalenceOfRingEquiv_counitIsostatement · cited by 0
- AlgCat.restrictScalarsEquivalenceOfRingEquiv_functorstatement · cited by 0
- AlgCat.restrictScalarsEquivalenceOfRingEquiv_inversestatement · cited by 0
- AlgCat.restrictScalarsEquivalenceOfRingEquiv_unitIsostatement · cited by 0
- AlgCat.restrictScalarsId'_hom_app_hom_applystatement · cited by 0
- AlgCat.restrictScalarsId'_inv_app_hom_applystatement · cited by 0
- AlgCat.restrictScalars_mapstatement and proof · cited by 0