Theorems · Theorem · commutative algebra
Subring.map_le_iff_le_comap
∀ {R : Type u} {S : Type v} [inst : NonAssocRing R] [inst_1 : NonAssocRing S] {f : R →+* S} {s : Subring R}
{t : Subring S}, Subring.map f s ≤ t ↔ s ≤ Subring.comap f t- Defined in
- Mathlib.Algebra.Ring.Subring.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
- Assumes
- NonAssocRingNonAssocRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Set.image_subset_iffproof · cited by 203
- Subring.mapstatement · cited by 33
- Subring.comapstatement · cited by 22
Cited by3
Results whose statement or proof uses this declaration.
- Subring.gc_map_comapproof · cited by 7
- CommRingCat.closure_range_union_range_eq_top_of_isPushoutproof · cited by 1
- Subring.comap_map_eqproof · cited by 1