Mathlib Map

Theorems · Definition · commutative algebra

AlgHom.toUnder

{R : CommRingCat} →
  {A B : Type u} →
    [inst : CommRing A] →
      [inst_1 : CommRing B] →
        [inst_2 : Algebra (↑R) A] → [inst_3 : Algebra (↑R) B] → (A →ₐ[↑R] B) → (R.mkUnder A ⟶ R.mkUnder B)

Make a morphism in Under R from an algebra map.

Defined in
Mathlib.Algebra.Category.Ring.Under.Basic
Cited by
10 results in Mathlib
Foundations
Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingCommRingAlgebraAlgebra

Around this declaration

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

commAlgCatEquivUnder · cited by 9commAlgCatEquivUnderCommRingCat.tensorProd · cited by 7CommRingCat.tensorProdCommRingCat.Under.equalizerFork · cited by 3Under.equalizerForkAlgEquiv.toUnder · cited by 3AlgEquiv.toUnderCommRingCat.Under.equalizerFork' · cited by 1Under.equalizerFork'CommRingCat.preservesLimit_parallelPair_tensorProd_iff_tensorEqualizer_bijective · cited by 1CommRingCat.preservesLimi…CommRingCat.Under.equalizer_comp · cited by 1Under.equalizer_compCommRingCat.Under.tensorProdEqualizer · cited by 1Under.tensorProdEqualizerCommRingCat.Under.equalizerFork'IsLimit · cited by 0Under.equalizerFork'IsLim…CommRingCat.Under.equalizerFork'_ι · cited by 0Under.equalizerFork'_ιCommRingCat.Under.equalizerFork_ι · cited by 0Under.equalizerFork_ιcommAlgCatEquivUnder_counitIso · cited by 0commAlgCatEquivUnder_coun…commAlgCatEquivUnder_functor_map · cited by 0commAlgCatEquivUnder_func…CommRingCat.Under.tensorProdEqualizer_ι · cited by 0Under.tensorProdEqualizer…CommRingCat.Under.tensorProductFan · cited by 0Under.tensorProductFanQuiver.Hom · cited by 32603Quiver.HomCommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraAlgHom · cited by 3236AlgHomCommRingCat · cited by 2333CommRingCatCommRingCat.carrier · cited by 1096CommRingCat.carrierAlgHom.toRingHom · cited by 490AlgHom.toRingHomCategoryTheory.Under · cited by 276CategoryTheory.UnderCommRingCat.ofHom · cited by 259CommRingCat.ofHomCategoryTheory.Under.homMk · cited by 43Under.homMkCommRingCat.mkUnder · cited by 24CommRingCat.mkUnderAlgHom.toUnderCITED BYCITES

Cites11

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

Cited by19

Results whose statement or proof uses this declaration.