Theorems · Definition · commutative algebra
CommRingCat.toAlgHom
{R : CommRingCat} → {A B : CategoryTheory.Under R} → (A ⟶ B) → ↑A.right →ₐ[↑R] ↑B.rightTurn a morphism in Under R into an algebra homomorphism.
- 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.
Cites9
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
- RingHomproof · cited by 10,189
- AlgHomstatement · cited by 3,236
- CommRingCatstatement and proof · cited by 2,333
- CommRingCat.carrierstatement and proof · cited by 1,096
- CommRingCat.Hom.homproof · cited by 432
- CategoryTheory.Understatement and proof · cited by 276
- CategoryTheory.Under.rightstatement and proof · cited by 128
- CategoryTheory.Under.Hom.rightproof · cited by 67
Cited by19
Results whose statement or proof uses this declaration.
- commAlgCatEquivUnderproof · cited by 9
- CommRingCat.tensorProdproof · cited by 7
- CommRingCat.Under.equalizerForkproof · cited by 3
- RingHom.HasStableEqualizers.preservesLimit_parallelPair_tensorProdproof · cited by 1
- CommRingCat.preservesLimit_parallelPair_tensorProd_iff_tensorEqualizer_bijectivestatement and proof · cited by 1
- CommRingCat.Under.equalizer_compstatement and proof · cited by 1
- CommRingCat.Under.tensorProdEqualizerproof · cited by 1
- CommRingCat.Under.equalizerForkTensorProdIsostatement and proof · cited by 0
- CommRingCat.Under.equalizerFork_ιstatement · cited by 0
- commAlgCatEquivUnder_counitIsostatement · cited by 0
- CommRingCat.Under.tensorProdEqualizer_ιstatement · cited by 0
- commAlgCatEquivUnder_inverse_mapstatement · cited by 0