Theorems · Definition · order theory
Setoid.quotientKerEquivOfSurjective
{α : Type u_1} → {β : Type u_2} → (f : α → β) → Function.Surjective f → Quotient (Setoid.ker f) ≃ βThe quotient of α by the kernel of a surjective function f bijects with f's codomain.
If a specific right-inverse of f is known, Setoid.quotientKerEquivOfRightInverse can be
definitionally more useful.
- Defined in
- Mathlib.Data.Setoid.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivstatement · cited by 8,337
- Function.surjInvproof · cited by 63
- Setoid.kerstatement · cited by 43
- Function.rightInverse_surjInvproof · cited by 11
- Setoid.quotientKerEquivOfRightInverseproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Topology.IsQuotientMap.homeomorphproof · cited by 5
- Setoid.quotientKerEquivOfSurjective.congr_simpstatement and proof · cited by 0