Theorems · Theorem · group theory
map_zero
∀ {M : Type u_4} {N : Type u_5} {F : Type u_9} [inst : Zero M] [inst_1 : Zero N] [inst_2 : FunLike F M N]
[ZeroHomClass F M N] (f : F), f 0 = 0- Defined in
- Mathlib.Algebra.Group.Hom.Defs
- Cited by
- 1,614 results in Mathlib
- Foundations
- Depth 5 from the axioms, rests on 12 definitions · uses no axioms
- Assumes
- ZeroZeroFunLikeZeroHomClass
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 · cited by 62,936
- FunLikestatement and proof · cited by 2,560
- ZeroHomClassstatement and proof · cited by 74
- ZeroHomClass.map_zeroproof · cited by 5
Cited by1,614
Results whose statement or proof uses this declaration.
- Polynomial.coeff_mapproof · cited by 114
- map_inv₀proof · cited by 106
- injective_iff_map_eq_zeroproof · cited by 62
- map_eq_zero_iffproof · cited by 62
- inner_zero_leftproof · cited by 59
- LinearMap.map_zeroproof · cited by 52
- Polynomial.eval₂_Cproof · cited by 50
- RingHom.map_zeroproof · cited by 47
- inner_zero_rightproof · cited by 40
- Polynomial.C_0proof · cited by 40
- TensorProduct.ext'proof · cited by 39
- Polynomial.derivative_mulproof · cited by 35
Showing the 200 most cited of 1,614.