From f23b3c0e5d72d65b60f8eb9611e2ccfff9b99412 Mon Sep 17 00:00:00 2001 From: Chloe Brown Date: Thu, 6 Jan 2022 18:27:05 +0000 Subject: I: 5: b: characterise epimorphisms of OfPreorder --- src/CatTheory/Category/Instance/Of/Properties/Preorder.agda | 6 ++++++ 1 file changed, 6 insertions(+) (limited to 'src/CatTheory/Category/Instance') 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 = _ -- cgit v1.2.3