summaryrefslogtreecommitdiff
diff options
context:
space:
mode:
authorChloe Brown <chloe.brown.00@outlook.com>2022-01-05 16:04:40 +0000
committerChloe Brown <chloe.brown.00@outlook.com>2022-01-05 16:04:40 +0000
commit3d72d984c0a1aa60f137d5380ea49b1d5716ea48 (patch)
tree36a7dc736b361c0bf519cdaec4c393f539494c3d
parent729a483d9ab25b0cfb2471b22d723960c7f21b0d (diff)
I: 2: a: show isomorphisms composei-1-c
-rw-r--r--src/CatTheory/Morphism/Properties.agda29
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