Theorems · Definition · group theory
AddCon.liftOn
{M : Type u_1} →
[inst : Add M] → {β : Sort u_4} → {c : AddCon M} → c.Quotient → (f : M → β) → (∀ (a b : M), c a b → f a = f b) → βThe function on the quotient by a congruence relation c
induced by a function that is constant on c's equivalence classes.
- Defined in
- Mathlib.GroupTheory.Congruence.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- Add
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- AddConstatement and proof · cited by 138
- AddCon.Quotientstatement and proof · cited by 54
- Quotient.liftOn'proof · cited by 19
Cited by4
Results whose statement or proof uses this declaration.
- AddCon.liftproof · cited by 14
- AddCon.liftOn.congr_simpstatement and proof · cited by 0
- AddCon.liftOn_coestatement · cited by 0
- CharacterModule.homEquiv_apply_applystatement · cited by 0