[Merged by Bors] - feat (FieldTheory/Adjoin): generalize IntermediateField.exists_algHom_of_splits#9392
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[Merged by Bors] - feat (FieldTheory/Adjoin): generalize IntermediateField.exists_algHom_of_splits#9392alreadydone wants to merge 4 commits intomasterfrom
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…m_of_splits` (#9392) + Extract from `Lifts.exists_lift_of_splits` a version that assumes integrality and splitting of minimal polynomial over an intermediate field (either actual IntermediateField or middle of IsScalarTower) rather than the base field + Generalize `exists_algHom_adjoin_of_splits`, `exists_algHom_of_adjoin_splits`, `exists_algHom_of_splits` to the same setting + Prove the [extension lemma](https://math.stackexchange.com/a/687914/12932) `surjective_comp_algebraMap_of_isAlgebraic/isSeparable` to be used in the proof that an epimorphism in the category of fields is a purely inseparable extension. Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>
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IntermediateField.exists_algHom_of_splitsIntermediateField.exists_algHom_of_splits
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Extract from
Lifts.exists_lift_of_splitsa version that assumes integrality and splitting of minimal polynomial over an intermediate field (either actual IntermediateField or middle of IsScalarTower) rather than the base fieldGeneralize
exists_algHom_adjoin_of_splits,exists_algHom_of_adjoin_splits,exists_algHom_of_splitsto the same settingProve the extension lemma
surjective_comp_algebraMap_of_isAlgebraic/isSeparableto be used in the proof that an epimorphism in the category of fields is a purely inseparable extension.