Theorems · Theorem · group theory
Con.map_apply
∀ {M : Type u_1} [inst : MulOneClass M] {c d : Con M} (h : c ≤ d) (x : c.Quotient), (c.map d h) x = (c.lift d.mk' ⋯) xGiven congruence relations c, d on a monoid such that d contains c, the definition of
the homomorphism from the quotient by c to the quotient by d induced by d's quotient map.
- Defined in
- Mathlib.GroupTheory.Congruence.Hom
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Quot.sound
- Assumes
- MulOneClass
Around this declaration
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- MonoidHomstatement · cited by 3,629
- MulOneClassstatement and proof · cited by 1,018
- Constatement and proof · cited by 152
- Con.Quotientstatement and proof · cited by 48
- Con.toQuotientstatement · cited by 33
- Con.mk'statement · cited by 22
- Con.liftstatement · cited by 12
- Con.eqstatement · cited by 9
- Con.mapstatement · cited by 1
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