Theorems · Theorem · ring theory

IsGroupLikeElem.map

∀ {F : Type u_1} {R : Type u_2} {A : Type u_3} {B : Type u_4} [inst : CommSemiring R] [inst_1 : AddCommMonoid A]
  [inst_2 : AddCommMonoid B] [inst_3 : Module R A] [inst_4 : Coalgebra R A] [inst_5 : Module R B]
  [inst_6 : Coalgebra R B] {a : A} [inst_7 : FunLike F A B] [CoalgHomClass F R A B] (f : F),
  IsGroupLikeElem R a → IsGroupLikeElem R (f a)

A coalgebra homomorphism sends group-like elements to group-like elements.

Defined in

Mathlib.RingTheory.Coalgebra.GroupLike

Cited by

1 results in Mathlib

Foundations

Depth 61 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidAddCommMonoidModuleCoalgebraModuleCoalgebraFunLikeCoalgHomClass