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Theorems · Theorem · commutative algebra

CommRingCat.hom_ext

∀ {R S : CommRingCat} {f g : R ⟶ S}, CommRingCat.Hom.hom f = CommRingCat.Hom.hom g → f = g
Defined in
Mathlib.Algebra.Category.Ring.Basic
Cited by
55 results in Mathlib
Foundations
Depth 24 from the axioms · uses propext, Quot.sound

Around this declaration

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

CommRingCat.hom_ext_iff · cited by 9CommRingCat.hom_ext_iffCommRingCat.isPushout_tensorProduct · cited by 7CommRingCat.isPushout_ten…AlgebraicGeometry.Scheme.Hom.normalizationDesc_comp · cited by 5Hom.normalizationDesc_compAlgebraicGeometry.LocallyRingedSpace.evaluation_naturality · cited by 4LocallyRingedSpace.evalua…AlgebraicGeometry.AffineSpace.SpecIso_inv_over · cited by 4AffineSpace.SpecIso_inv_o…AlgebraicGeometry.localRingHom_comp_stalkIso · cited by 3AlgebraicGeometry.localRi…AlgebraicGeometry.Scheme.residue_descResidueField · cited by 3Scheme.residue_descResidu…AlgebraicGeometry.stalkClosedPointIso_inv · cited by 3AlgebraicGeometry.stalkCl…AlgebraicGeometry.StructureSheaf.toOpen_comp_comap · cited by 3StructureSheaf.toOpen_com…CommRingCat.HomTopology.isEmbedding_precomp_of_surjective · cited by 2HomTopology.isEmbedding_p…CommRingCat.epi_iff_epi · cited by 2CommRingCat.epi_iff_epiAlgebraicGeometry.isIso_pushoutSection_of_iSup_eq · cited by 2AlgebraicGeometry.isIso_p…AlgebraicGeometry.IsAffineOpen.appLE_eq_away_map · cited by 2IsAffineOpen.appLE_eq_awa…AlgebraicGeometry.Proj.awayMap_awayToSection · cited by 2Proj.awayMap_awayToSectionAlgebraicGeometry.Proj.awayToSection_comp_appLE · cited by 2Proj.awayToSection_comp_a…Quiver.Hom · cited by 32603Quiver.HomRingHom · cited by 10189RingHomCommRingCat · cited by 2333CommRingCatCommRingCat.carrier · cited by 1096CommRingCat.carrierCommRingCat.Hom.hom · cited by 432Hom.homCommRingCat.Hom.ext · cited by 2Hom.extCommRingCat.hom_extCITED BYCITES

Cites6

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

Cited by55

Results whose statement or proof uses this declaration.