Theorems · Theorem · commutative algebra
Subring.gc_map_comap
∀ {R : Type u} {S : Type v} [inst : NonAssocRing R] [inst_1 : NonAssocRing S] (f : R →+* S),
GaloisConnection (Subring.map f) (Subring.comap f)- Defined in
- Mathlib.Algebra.Ring.Subring.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
- Assumes
- NonAssocRingNonAssocRing
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
- Subringstatement and proof · cited by 602
- NonAssocRingstatement and proof · cited by 483
- GaloisConnectionstatement · cited by 253
- Subring.mapstatement · cited by 33
- Subring.comapstatement · cited by 22
- Subring.map_le_iff_le_comapproof · cited by 3
Cited by7
Results whose statement or proof uses this declaration.
- RingHom.map_closureproof · cited by 4
- Subring.map_supproof · cited by 2
- Subring.map_botproof · cited by 1
- Subring.comap_topproof · cited by 1
- Subring.comap_iInfproof · cited by 0
- Subring.comap_infproof · cited by 0
- Subring.map_iSupproof · cited by 0