Investigations on graph-theoretical constructions in Homotopy type theory

{-# OPTIONS --without-K --exact-split #-}

module lib.graph-homomorphisms.classes.Isomorphisms.Exponentiation
  where
  open import foundations.Core
  open import lib.graph-definitions.Graph
  open import lib.graph-relations.Isomorphic
  open import lib.graph-calculation-reasoning.Isos

  private
    variable
     ℓ : Level

  module
    _
    (G : Graph ℓ)
    where

    expo-iso
      : (iso : G ≅ G) → ℕ
      → G ≅ G
    expo-iso iso zero = idEqv , λ x y → idEqv
    expo-iso iso (succ n) = ≅-trans {A = G}{B = G}{C = G} (expo-iso iso n) iso

    syntax expo-iso iso n = iso ^-iso n

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