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Minor reasoning combinator updates #464

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Merged
JacquesCarette merged 2 commits into from
May 6, 2025
Merged

Minor reasoning combinator updates #464

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cdf40a1
Add more 'missing' merge combinators
jacquescomeaux May 5, 2025
51ae6c4
Flip direction of push-center argument
jacquescomeaux May 5, 2025
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10 changes: 9 additions & 1 deletion src/Categories/Category/Monoidal/Reasoning.agda
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Original file line number Diff line number Diff line change
Expand Up @@ -135,7 +135,15 @@ split₂ˡ {f = f} {g} {h} = begin
id ⊗₁ g ∘ f ⊗₁ h ∎

-- The opposite, i.e. merge
merge₂ʳ : ∀ {X₁ Y₁ X₂ Y₂ Z₂} {f : X₁ ⇒ Y₁} {g : Y₂ ⇒ Z₂} {h : X₂ ⇒ Y₂} →
merge₁ʳ : ∀ {X₁ Y₁ Z₁ X₂ Y₂} {f : Y₁ ⇒ Z₁} {g : X₁ ⇒ Y₁} {h : X₂ ⇒ Y₂} →
f ⊗₁ h ∘ g ⊗₁ id ≈ (f ∘ g) ⊗₁ h
merge₁ʳ = Equiv.sym split₁ʳ

merge₁ˡ : ∀ {X₁ Y₁ Z₁ X₂ Y₂} {f : Y₁ ⇒ Z₁} {g : X₁ ⇒ Y₁} {h : X₂ ⇒ Y₂} →
f ⊗₁ id ∘ g ⊗₁ h ≈ (f ∘ g) ⊗₁ h
merge₁ˡ = Equiv.sym split₁ˡ

merge₂ʳ : ∀ {X₁ Y₁ X₂ Y₂ Z₂} {f : X₁ ⇒ Y₁} {g : Y₂ ⇒ Z₂} {h : X₂ ⇒ Y₂} →
f ⊗₁ g ∘ id ⊗₁ h ≈ f ⊗₁ (g ∘ h)
merge₂ʳ = Equiv.sym split₂ʳ

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4 changes: 2 additions & 2 deletions src/Categories/Morphism/Reasoning/Core.agda
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Expand Up @@ -309,8 +309,8 @@ pull-first {f = f} {g = g} {a = a} {h = h} {i = i} eq = begin
pull-center : g ∘ h ≈ a → f ∘ (g ∘ (h ∘ i)) ≈ f ∘ (a ∘ i)
pull-center eq = ∘-resp-≈ʳ (pullˡ eq)

push-center : g ∘ h ≈ a → f ∘ (a ∘ i) ≈ f ∘ (g ∘ (h ∘ i))
push-center eq = Equiv.sym (pull-center eq)
push-center : a ≈ g ∘ h → f ∘ (a ∘ i) ≈ f ∘ (g ∘ (h ∘ i))
push-center eq = Equiv.sym (pull-center (Equiv.sym eq))

intro-first : a ∘ b ≈ id → f ∘ g ≈ a ∘ ((b ∘ f) ∘ g)
intro-first {a = a} {b = b} {f = f} {g = g} eq = begin
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