Theorems · Theorem · group theory
MonoidHom.map_one
∀ {M : Type u_4} {N : Type u_5} [inst : MulOne M] [inst_1 : MulOne N] (f : M →* N), f 1 = 1If f is a monoid homomorphism then f 1 = 1.
- Defined in
- Mathlib.Algebra.Group.Hom.Defs
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
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.
- DFunLike.coestatement · cited by 62,936
- MonoidHomstatement and proof · cited by 3,629
- MonoidHom.toOneHomproof · cited by 132
- MulOnestatement and proof · cited by 65
- OneHom.map_one'proof · cited by 4
Cited by27
Results whose statement or proof uses this declaration.
- MonoidHom.ker_eq_bot_iffproof · cited by 16
- orderOf_injectiveproof · cited by 12
- FreeMonoid.hom_eqproof · cited by 7
- LinearMap.det_idproof · cited by 7
- CategoryTheory.MonObj.comp_oneproof · cited by 7
- MonoidHom.isOfFinOrderproof · cited by 6
- IsPGroup.of_surjectiveproof · cited by 3
- MonoidHom.map_finprod_of_injectiveproof · cited by 3
- MonoidHom.map_finprod_pliftproof · cited by 3
- linearIndependent_monoidHomproof · cited by 3
- IsPGroup.of_injectiveproof · cited by 2
- MonoidHom.map_finprod_of_preimage_oneproof · cited by 2