Theorems · Theorem · field theory
Subfield.gc_map_comap
∀ {K : Type u} {L : Type v} [inst : DivisionRing K] [inst_1 : DivisionRing L] (f : K →+* L),
GaloisConnection (Subfield.map f) (Subfield.comap f)- Defined in
- Mathlib.Algebra.Field.Subfield.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DivisionRingDivisionRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHomstatement and proof · cited by 10,189
- DivisionRingstatement and proof · cited by 1,062
- Subfieldstatement and proof · cited by 303
- GaloisConnectionstatement · cited by 253
- Subfield.mapstatement · cited by 30
- Subfield.comapstatement · cited by 29
- Subfield.map_le_iff_le_comapproof · cited by 1
Cited by7
Results whose statement or proof uses this declaration.
- Subfield.map_botproof · cited by 3
- RingHom.map_field_closureproof · cited by 1
- Subfield.comap_iInfproof · cited by 0
- Subfield.comap_infproof · cited by 0
- Subfield.map_supproof · cited by 0
- Subfield.comap_topproof · cited by 0
- Subfield.map_iSupproof · cited by 0