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Add computation rules to suspension and pushout #52

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Add computation rules to suspension and pushout #52

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bae6a06
Add computation rules to suspension and pushout
TimonNajdovski May 1, 2023
fe92833
Update Lecture4-notes.lagda.md
TimonNajdovski May 1, 2023
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19 changes: 16 additions & 3 deletions Agda/HITs/Lecture4-notes.lagda.md
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Original file line number Diff line number Diff line change
Expand Up @@ -302,7 +302,16 @@ postulate
merid : {A : Type} → A → northS ≡ southS [ Susp A ]
Susp-rec : {l : Level} {A : Type} {X : Type l}
(n : X) (s : X) (m : A → n ≡ s)
→ Susp A → X
→ Susp A → X
Susp-rec-north : {l : Level} {A : Type} {X : Type l} (n : X) (s : X) (m : A → n ≡ s)
→ Susp-rec n s m northS ≡ n
Susp-rec-south : {l : Level} {A : Type} {X : Type l} (n : X) (s : X) (m : A → n ≡ s)
→ Susp-rec n s m southS ≡ s
{-# REWRITE Susp-rec-north #-}
{-# REWRITE Susp-rec-south #-}
postulate
Susp-rec-meridan : {l : Level} {A : Type} {X : Type l} (n : X) (s : X) (m : A → n ≡ s)
→ (a : A) → ap (Susp-rec n s m) (merid a) ≡ m a
```

# Pushouts
Expand All @@ -318,8 +327,12 @@ module _ {C : Type} {A : Type} {B : Type} {f : C → A} {g : C → B} where
inr : B → Pushout C A B f g
glue : (c : C) → inl (f c) ≡ inr (g c)
Push-rec : {X : Type} (l : A → X) (r : B → X) (gl : (c : C) → l (f c) ≡ r (g c))
→ Pushout C A B f g → X
```
→ Pushout C A B f g → X
Push-rec-glue-l : {X : Type} (l : A → X) (r : B → X) (gl : (c : C) → l (f c) ≡ r (g c))
→ (a : A) → (Push-rec l r gl) (inl a) ≡ l a
Push-rec-glue-r : {X : Type} (l : A → X) (r : B → X) (gl : (c : C) → l (f c) ≡ r (g c))
→ (b : B) → (Push-rec l r gl) (inr b) ≡ r b
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@ncfavier ncfavier May 1, 2023 •
edited
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These should be named Push-rec-in{l,r} and there should be a separate rule relating glue and gl.

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You marked this as resolved, did you forget to push the update?

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I marked it as resolved accidentaly, sorry. Thank you for the correction, the update should be pushed now.

```

# Relation quotient

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