diff options
author | Chloe Brown <chloe.brown.00@outlook.com> | 2022-01-05 16:04:40 +0000 |
---|---|---|
committer | Chloe Brown <chloe.brown.00@outlook.com> | 2022-01-05 16:04:40 +0000 |
commit | 3d72d984c0a1aa60f137d5380ea49b1d5716ea48 (patch) | |
tree | 36a7dc736b361c0bf519cdaec4c393f539494c3d | |
parent | 729a483d9ab25b0cfb2471b22d723960c7f21b0d (diff) |
I: 2: a: show isomorphisms composei-1-c
-rw-r--r-- | src/CatTheory/Morphism/Properties.agda | 29 |
1 files changed, 29 insertions, 0 deletions
diff --git a/src/CatTheory/Morphism/Properties.agda b/src/CatTheory/Morphism/Properties.agda new file mode 100644 index 0000000..d0a6e7b --- /dev/null +++ b/src/CatTheory/Morphism/Properties.agda @@ -0,0 +1,29 @@ +{-# OPTIONS --without-K --safe #-} +open import Categories.Category + +module CatTheory.Morphism.Properties {o ℓ e} (𝒞 : Category o ℓ e) where + +open Category 𝒞 +open HomReasoning + +import Categories.Morphism as M +open M 𝒞 +open import Categories.Morphism.Reasoning 𝒞 + +private + variable + A B C D : Obj + f g h i : A ⇒ B + +Iso-∘ : Iso f g → Iso h i → Iso (f ∘ h) (i ∘ g) +Iso-∘ {f = f} {g = g} {h = h} {i = i} iso₁ iso₂ = record + { isoˡ = begin + (i ∘ g) ∘ f ∘ h ≈⟨ cancelInner iso₁.isoˡ ⟩ + i ∘ h ≈⟨ iso₂.isoˡ ⟩ + id ∎ + ; isoʳ = begin + (f ∘ h) ∘ i ∘ g ≈⟨ cancelInner iso₂.isoʳ ⟩ + f ∘ g ≈⟨ iso₁.isoʳ ⟩ + id ∎ + } + where module iso₁ = Iso iso₁; module iso₂ = Iso iso₂ |