Theorems · Definition · group theory
Con.quotientQuotientEquivQuotient
{M : Type u_1} → [inst : MulOneClass M] → (c d : Con M) → (h : c ≤ d) → (Con.ker (c.map d h)).Quotient ≃* d.QuotientThe third isomorphism theorem for monoids.
- Defined in
- Mathlib.GroupTheory.Congruence.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Quot.sound
- Assumes
- MulOneClass
Around this declaration
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivproof · cited by 8,337
- MonoidHomstatement · cited by 3,629
- MulEquivstatement · cited by 1,142
- MulOneClassstatement and proof · cited by 1,018
- Constatement and proof · cited by 152
- Con.Quotientstatement · cited by 48
- Setoid.kerproof · cited by 43
- Con.toSetoidproof · cited by 38
- Con.kerstatement · cited by 24
- Con.mapstatement · cited by 1
- Quot.mapRightproof · cited by 0
- Setoid.quotientQuotientEquivQuotientproof · cited by 0
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