{-# OPTIONS --safe --warning=error --without-K #-}

open import LogicalFormulae
open import Setoids.Setoids
open import Functions
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Numbers.Naturals.Naturals
open import Sets.FinSet
open import Groups.Definition
open import Groups.Homomorphisms.Definition

module Groups.Subgroups.Definition where

record Subgroup {a} {b} {c} {d} {A : Set a} {B : Set c} {S : Setoid {a} {b} A} {T : Setoid {c} {d} B} {_·A_ : A → A → A} {_·B_ : B → B → B} (G : Group S _·A_) (H : Group T _·B_) {f : B → A} (hom : GroupHom H G f) : Set (a ⊔ b ⊔ c ⊔ d) where
  open Setoid T renaming (_∼_ to _∼G_)
  open Setoid S renaming (_∼_ to _∼H_)
  field
    fInj : SetoidInjection T S f