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Theorems · Theorem · group theory

MonoidWithZeroHom.comp_one

∀ {M₀ : Type u_1} {N₀ : Type u_2} {G₀ : Type u_3} [inst : MulZeroOneClass M₀] [inst_1 : Nontrivial M₀]
  [inst_2 : NoZeroDivisors M₀] [inst_3 : MulZeroOneClass N₀] [inst_4 : MulZeroOneClass G₀]
  [inst_5 : DecidablePred fun x => x = 0] (f : N₀ →*₀ G₀), f.comp 1 = 1

The trivial group-with-zero hom is absorbing for composition.

Defined in
Mathlib.Algebra.GroupWithZero.WithZero
Cited by
0 results in Mathlib
Foundations
Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MulZeroOneClassNontrivialNoZeroDivisorsMulZeroOneClassMulZeroOneClassDecidablePred
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Nontrivial · cited by 2416NontrivialMonoidWithZeroHom · cited by 704MonoidWithZeroHomNoZeroDivisors · cited by 545NoZeroDivisorsMulZeroOneClass · cited by 184MulZeroOneClassMonoidWithZeroHom.comp · cited by 34MonoidWithZeroHom.compMonoidWithZeroHom.ext · cited by 15MonoidWithZeroHom.extMonoidWithZeroHom.apply_one_apply_eq · cited by 1MonoidWithZeroHom.apply_o…MonoidWithZeroHom.comp_oneCITED BYCITES

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