Theorems · Theorem · commutative algebra
Subsemiring.gc_map_comap
∀ {R : Type u} {S : Type v} [inst : NonAssocSemiring R] [inst_1 : NonAssocSemiring S] (f : R →+* S),
GaloisConnection (Subsemiring.map f) (Subsemiring.comap f)- Defined in
- Mathlib.Algebra.Ring.Subsemiring.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
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
- NonAssocSemiringstatement and proof · cited by 805
- Subsemiringstatement and proof · cited by 456
- GaloisConnectionstatement · cited by 253
- Subsemiring.mapstatement · cited by 29
- Subsemiring.comapstatement · cited by 20
- Subsemiring.map_le_iff_le_comapproof · cited by 1
Cited by7
Results whose statement or proof uses this declaration.
- Subsemiring.comap_topproof · cited by 1
- Subsemiring.map_supproof · cited by 1
- RingHom.map_closureSproof · cited by 1
- Subsemiring.map_botproof · cited by 1
- Subsemiring.comap_infproof · cited by 0
- Subsemiring.comap_iInfproof · cited by 0
- Subsemiring.map_iSupproof · cited by 0