Theorems · Definition · field theory
Field.Emb.Cardinal.embFunctor
(F : Type u) →
(E : Type v) →
[inst : Field F] →
[inst_1 : Field E] →
[inst_2 : Algebra F E] →
[rank_inf : Fact (Cardinal.aleph0 ≤ Module.rank F E)] →
[inst_3 : Algebra.IsAlgebraic F E] →
⦃i j : WithTop (Module.rank F E).ord.ToType⦄ →
i ≤ j →
(↥(Field.Emb.Cardinal.filtration j) →ₐ[F] AlgebraicClosure E) →
↥(Field.Emb.Cardinal.filtration i) →ₐ[F] AlgebraicClosure EThe functor on WithTop ι given by embeddings of E⟮<i⟯ into Ē
- Defined in
- Mathlib.FieldTheory.CardinalEmb
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- WithTopstatement and proof · cited by 3,754
- AlgHomstatement and proof · cited by 3,236
- Factstatement and proof · cited by 2,726
- Cardinalstatement · cited by 2,598
- IntermediateFieldstatement · cited by 988
- OrderEmbeddingstatement · cited by 619
- Cardinal.aleph0statement and proof · cited by 521
- AlgHom.compproof · cited by 501
- Module.rankstatement and proof · cited by 496
Cited by4
Results whose statement or proof uses this declaration.
- Field.Emb.Cardinal.equivLimstatement and proof · cited by 1
- Field.Emb.Cardinal.equivLim_coherencestatement · cited by 0
- Field.Emb.Cardinal.equivSucc_coherencestatement · cited by 0
- Field.Emb.Cardinal.embFunctor.congr_simpstatement and proof · cited by 0