diff options
| author | Chloe Brown <chloe.brown.00@outlook.com> | 2022-01-06 18:27:05 +0000 |
|---|---|---|
| committer | Chloe Brown <chloe.brown.00@outlook.com> | 2022-01-06 18:27:05 +0000 |
| commit | f23b3c0e5d72d65b60f8eb9611e2ccfff9b99412 (patch) | |
| tree | db3ab06731050e13e4486fb129623e8241dcdfaf | |
| parent | 96e2e835b509c7a159a65d9c7c3e653577b2bd83 (diff) | |
I: 5: b: characterise epimorphisms of OfPreorder
| -rw-r--r-- | src/CatTheory/Category/Instance/Of/Properties/Preorder.agda | 6 |
1 files changed, 6 insertions, 0 deletions
diff --git a/src/CatTheory/Category/Instance/Of/Properties/Preorder.agda b/src/CatTheory/Category/Instance/Of/Properties/Preorder.agda index 025964f..da9e083 100644 --- a/src/CatTheory/Category/Instance/Of/Properties/Preorder.agda +++ b/src/CatTheory/Category/Instance/Of/Properties/Preorder.agda @@ -16,3 +16,9 @@ open import Categories.Morphism (OfPreorder P) sym⇒retract : ∀ {A B} {f : A ∼ B} {g : B ∼ A} → g RetractOf f sym⇒retract = _ + +∀-Epi : ∀ {A B} {f : A ∼ B} → Epi f +∀-Epi = _ + +sym⇒section : ∀ {A B} {f : A ∼ B} {g : B ∼ A} → g SectionOf f +sym⇒section = _ |