Theorems · Definition · group theory
QuotientAddGroup.kerLift
{G : Type u} → [inst : AddGroup G] → {H : Type v} → [inst_1 : AddGroup H] → (φ : G →+ H) → G ⧸ φ.ker →+ HThe induced map from the quotient by the kernel to the codomain.
- Defined in
- Mathlib.GroupTheory.QuotientGroup.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- AddMonoidHomstatement and proof · cited by 3,230
- HasQuotient.Quotientstatement · cited by 2,301
- AddMonoidHom.kerstatement and proof · cited by 158
- QuotientAddGroup.liftproof · cited by 15
Cited by6
Results whose statement or proof uses this declaration.
- QuotientAddGroup.quotientKerEquivOfRightInverseproof · cited by 2
- AddMonoidHom.isStrictMap_iff_isEmbedding_kerLiftstatement and proof · cited by 1
- QuotientAddGroup.kerLift_injectivestatement · cited by 1
- QuotientAddGroup.quotientBot_applystatement · cited by 0
- QuotientAddGroup.quotientKerEquivOfRightInverse_applystatement · cited by 0
- QuotientAddGroup.kerLift_mkstatement · cited by 0