Theorems · Definition · order theory
sSupHom.dual
{α : Type u_2} → {β : Type u_3} → [inst : SupSet α] → [inst_1 : SupSet β] → sSupHom α β ≃ sInfHom αᵒᵈ βᵒᵈReinterpret a ⨆-homomorphism as an ⨅-homomorphism between the dual orders.
- Defined in
- Mathlib.Order.Hom.CompleteLattice
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Equivstatement · cited by 8,337
- OrderDualstatement and proof · cited by 927
- OrderDual.toDualproof · cited by 481
- OrderDual.ofDualproof · cited by 400
- SupSetstatement and proof · cited by 154
- sInfHomstatement and proof · cited by 43
- sSupHomstatement and proof · cited by 40
- sSupHom.map_sSup'proof · cited by 0
Cited by8
Results whose statement or proof uses this declaration.
- CompleteLatticeHom.dualproof · cited by 8
- sSupHom.dual_idstatement · cited by 0
- sSupHom.dual_symm_apply_toFunstatement and proof · cited by 0
- sSupHom.symm_dual_compstatement · cited by 0
- sSupHom.symm_dual_idstatement · cited by 0
- sSupHom.continuousproof · cited by 0
- sSupHom.dual_apply_toFunstatement and proof · cited by 0
- sSupHom.dual_compstatement · cited by 0