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Theorems · Definition · commutative algebra

CommRingCat.toAlgHom

{R : CommRingCat} → {A B : CategoryTheory.Under R} → (A ⟶ B) → ↑A.right →ₐ[↑R] ↑B.right

Turn a morphism in Under R into an algebra homomorphism.

Defined in
Mathlib.Algebra.Category.Ring.Under.Basic
Cited by
13 results in Mathlib
Foundations
Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

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.equalizerForkRingHom.HasStableEqualizers.preservesLimit_parallelPair_tensorProd · cited by 1HasStableEqualizers.prese…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.equalizerForkTensorProdIso · cited by 0Under.equalizerForkTensor…CommRingCat.Under.equalizerFork_ι · cited by 0Under.equalizerFork_ιcommAlgCatEquivUnder_counitIso · cited by 0commAlgCatEquivUnder_coun…CommRingCat.Under.tensorProdEqualizer_ι · cited by 0Under.tensorProdEqualizer…commAlgCatEquivUnder_inverse_map · cited by 0commAlgCatEquivUnder_inve…CommRingCat.Under.tensorProdMapEqualizerForkIsLimit · cited by 0Under.tensorProdMapEquali…commAlgCatEquivUnder_unitIso · cited by 0commAlgCatEquivUnder_unit…CommRingCat.tensorProd_map_right · cited by 0CommRingCat.tensorProd_ma…Quiver.Hom · cited by 32603Quiver.HomRingHom · cited by 10189RingHomAlgHom · cited by 3236AlgHomCommRingCat · cited by 2333CommRingCatCommRingCat.carrier · cited by 1096CommRingCat.carrierCommRingCat.Hom.hom · cited by 432Hom.homCategoryTheory.Under · cited by 276CategoryTheory.UnderCategoryTheory.Under.right · cited by 128Under.rightCategoryTheory.Under.Hom.right · cited by 67Hom.rightCommRingCat.toAlgHomCITED BYCITES

Cites9

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.