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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
Assumes
CommRingCommRing

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgCat.restrictScalarsComp' · cited by 4AlgCat.restrictScalarsCom…AlgCat.restrictScalarsEquivalenceOfRingEquiv · cited by 4AlgCat.restrictScalarsEqu…AlgCat.restrictScalarsId' · cited by 4AlgCat.restrictScalarsId'AlgCat.restrictScalarsComp'_hom_app_hom_apply · cited by 0AlgCat.restrictScalarsCom…AlgCat.restrictScalarsComp'_inv_app_hom_apply · cited by 0AlgCat.restrictScalarsCom…AlgCat.restrictScalarsEquivalenceOfRingEquiv_counitIso · cited by 0AlgCat.restrictScalarsEqu…AlgCat.restrictScalarsEquivalenceOfRingEquiv_functor · cited by 0AlgCat.restrictScalarsEqu…AlgCat.restrictScalarsEquivalenceOfRingEquiv_inverse · cited by 0AlgCat.restrictScalarsEqu…AlgCat.restrictScalarsEquivalenceOfRingEquiv_unitIso · cited by 0AlgCat.restrictScalarsEqu…AlgCat.restrictScalarsId'_hom_app_hom_apply · cited by 0AlgCat.restrictScalarsId'…AlgCat.restrictScalarsId'_inv_app_hom_apply · cited by 0AlgCat.restrictScalarsId'…AlgCat.restrictScalars_map · cited by 0AlgCat.restrictScalars_mapAlgCat.restrictScalars_obj_carrier · cited by 0AlgCat.restrictScalars_ob…Quiver.Hom · cited by 32603Quiver.HomCommRing · cited by 17173CommRingCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorRingHom · cited by 10189RingHomAlgHom.restrictScalars · cited by 83AlgHom.restrictScalarsAlgCat · cited by 75AlgCatAlgCat.carrier · cited by 61AlgCat.carrierAlgCat.Hom.hom · cited by 27Hom.homAlgCat.of · cited by 23AlgCat.ofAlgCat.ofHom · cited by 16AlgCat.ofHomAlgCat.restrictScalarsCITED BYCITES

Cites10

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

Cited by13

Results whose statement or proof uses this declaration.