Theorems · Definition · group theory

Function.Injective.mulActionHom_embedding

{G : Type u_1} →
  {α : Type u_2} →
    [inst : Group G] →
      [inst_1 : MulAction G α] →
        {H : Type u_3} →
          {β : Type u_4} →
            [inst_2 : Group H] →
              [inst_3 : MulAction H β] →
                {σ : G → H} → {f : α →ₑ[σ] β} → (ι : Type u_5) → Function.Injective ⇑f → (ι ↪ α) →ₑ[σ] ι ↪ β

An injective equivariant map α →ₑ[σ] β induces an equivariant map on embedding types (ι ↪ α) → (ι ↪ β).

Defined in

Mathlib.GroupTheory.GroupAction.MultipleTransitivity

Cited by

4 results in Mathlib

Foundations

Depth 18 from the axioms · uses propext, Quot.sound

Assumes

GroupMulActionGroupMulAction