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| author | Chloe Brown <chloe.brown.00@outlook.com> | 2022-01-05 19:20:37 +0000 |
|---|---|---|
| committer | Chloe Brown <chloe.brown.00@outlook.com> | 2022-01-05 19:20:37 +0000 |
| commit | 60e43c84effcefcb154aafca087328c9ee2395a4 (patch) | |
| tree | e9efb0d332c2d2e0ff9fda4dc21fb50a25afbcc9 | |
| parent | 8dd4b315a849aacc4d63d466edb3b634daf300cc (diff) | |
I: 4: f: characterise monomorphisms of OfPreorder
| -rw-r--r-- | src/CatTheory/Category/Instance/Of/Properties/Preorder.agda | 18 |
1 files changed, 18 insertions, 0 deletions
diff --git a/src/CatTheory/Category/Instance/Of/Properties/Preorder.agda b/src/CatTheory/Category/Instance/Of/Properties/Preorder.agda new file mode 100644 index 0000000..025964f --- /dev/null +++ b/src/CatTheory/Category/Instance/Of/Properties/Preorder.agda @@ -0,0 +1,18 @@ +{-# OPTIONS --without-K --safe #-} + +open import Relation.Binary.Bundles using (Preorder) + +module CatTheory.Category.Instance.Of.Properties.Preorder + {a l₁ l₂} + (P : Preorder a l₁ l₂) + where + +open import CatTheory.Category.Instance.Of.Preorder +open Preorder P +open import Categories.Morphism (OfPreorder P) + +∀-Mono : ∀ {A B} {f : A ∼ B} → Mono f +∀-Mono = _ + +sym⇒retract : ∀ {A B} {f : A ∼ B} {g : B ∼ A} → g RetractOf f +sym⇒retract = _ |