Principal group actions

module group-theory.principal-group-actions where

Imports

open import foundation.dependent-pair-types
open import foundation.equivalence-extensionality
open import foundation.universe-levels

open import group-theory.group-actions
open import group-theory.groups

Idea

The principal group action is the action of a group on itself by multiplication from the left

Definition

module _
  {l1 : Level} (G : Group l1)
  where

  principal-Abstract-Group-Action : Abstract-Group-Action G l1
  pr1 principal-Abstract-Group-Action = set-Group G
  pr1 (pr2 principal-Abstract-Group-Action) g = equiv-mul-Group G g
  pr2 (pr2 principal-Abstract-Group-Action) g h =
    eq-htpy-equiv (associative-mul-Group G g h)