Theorems · Definition · order theory
Setoid.comap
{α : Type u_1} → {β : Type u_2} → (α → β) → Setoid β → Setoid αGiven a function f : α → β, an equivalence relation r on β induces an equivalence
relation on α defined by 'x ≈ y iff f(x) is related to f(y) by r'.
See note [reducible non-instances].
- Defined in
- Mathlib.Data.Setoid.Basic
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Function.onFunproof · cited by 570
Cited by29
Results whose statement or proof uses this declaration.
- Con.comapproof · cited by 15
- AddCon.comapproof · cited by 14
- DiscreteQuotient.comapproof · cited by 3
- Setoid.comap_injectivestatement and proof · cited by 2
- Setoid.comap_relstatement · cited by 2
- LocallyConstant.discreteQuotientproof · cited by 2
- inseparableSetoidproof · cited by 2
- Setoid.comap_map_eqstatement · cited by 1
- Setoid.comap_map_of_ker_lestatement · cited by 1
- Setoid.comap_rel_eqstatement · cited by 1
- Setoid.le_comap_mapstatement · cited by 1
- projectivizationSetoidproof · cited by 1