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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- RingHomstatement · cited by 10,189
- CommRingCatstatement and proof · cited by 2,333
- CommRingCat.carrierstatement · cited by 1,096
- CommRingCat.Hom.homstatement and proof · cited by 432
- CommRingCat.Hom.extproof · cited by 2
Cited by55
Results whose statement or proof uses this declaration.
- CommRingCat.hom_ext_iffproof · cited by 9
- CommRingCat.isPushout_tensorProductproof · cited by 7
- AlgebraicGeometry.Scheme.Hom.normalizationDesc_compproof · cited by 5
- AlgebraicGeometry.LocallyRingedSpace.evaluation_naturalityproof · cited by 4
- AlgebraicGeometry.AffineSpace.SpecIso_inv_overproof · cited by 4
- AlgebraicGeometry.localRingHom_comp_stalkIsoproof · cited by 3
- AlgebraicGeometry.Scheme.residue_descResidueFieldproof · cited by 3
- AlgebraicGeometry.stalkClosedPointIso_invproof · cited by 3
- AlgebraicGeometry.StructureSheaf.toOpen_comp_comapproof · cited by 3
- CommRingCat.HomTopology.isEmbedding_precomp_of_surjectiveproof · cited by 2
- CommRingCat.epi_iff_epiproof · cited by 2
- AlgebraicGeometry.isIso_pushoutSection_of_iSup_eqproof · cited by 2