Theorems · Theorem · ring theory
Algebra.ext_id
∀ {R : Type u} (A : Type v) [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] (f g : R →ₐ[R] A),
f = gThis ext lemma closes trivial subgoals created when chaining heterobasic ext lemmas.
- Defined in
- Mathlib.Algebra.Algebra.Hom
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- AlgHomstatement and proof · cited by 3,236
Cited by17
Results whose statement or proof uses this declaration.
- MvPolynomial.algHom_extproof · cited by 55
- Algebra.comp_ofIdproof · cited by 3
- DualNumber.algHom_extproof · cited by 2
- Algebra.TensorProduct.includeLeft_bijectiveproof · cited by 2
- Algebra.IsUnramifiedAt.exists_notMem_forall_ne_mem_and_adjoin_eq_topproof · cited by 1
- Algebra.FormallySmooth.iff_of_surjectiveproof · cited by 1
- Algebra.IsSmoothAt.of_formallySmooth_fiberproof · cited by 1
- MonoidAlgebra.mapDomainBialgHom_mapDomainOfBialgHomproof · cited by 1
- Algebra.exists_etale_isIdempotentElem_forall_liesOver_eqproof · cited by 1
- ContinuousAlgHom.ext_ringproof · cited by 1
- AddMonoidAlgebra.mapDomainBialgHom_mapDomainOfBialgHomproof · cited by 1