Theorems · Definition · order theory
Sublattice.map
{α : Type u_2} →
{β : Type u_3} → [inst : Lattice α] → [inst_1 : Lattice β] → LatticeHom α β → Sublattice α → Sublattice βThe image of a sublattice along a monoid homomorphism is a sublattice.
- Defined in
- Mathlib.Order.Sublattice
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
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.
- DFunLike.coeproof · cited by 62,936
- SetLike.coeproof · cited by 8,199
- Set.imageproof · cited by 5,609
- Latticestatement and proof · cited by 916
- Sublatticestatement and proof · cited by 225
- LatticeHomstatement and proof · cited by 192
Cited by21
Results whose statement or proof uses this declaration.
- Sublattice.gc_map_comapstatement · cited by 6
- Sublattice.map_equiv_eq_comap_symmstatement and proof · cited by 1
- Sublattice.map_le_iff_le_comapstatement · cited by 1
- Sublattice.map_monostatement · cited by 1
- Sublattice.mem_map_of_memstatement · cited by 1
- Sublattice.LatticeHom.rangeproof · cited by 1
- Sublattice.apply_coe_mem_mapstatement · cited by 0
- Sublattice.apply_mem_map_iffstatement · cited by 0
- Sublattice.map_botstatement · cited by 0
- Sublattice.map_iSupstatement · cited by 0
- Sublattice.map_idstatement and proof · cited by 0
- Sublattice.map_infstatement · cited by 0