Total products #459
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Total products #459
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ncfavier
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Feb 2, 2025
plt-amy
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Feb 5, 2025
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| record is-total-product | ||
| {x y p} {x' : Ob[ x ]} {y' : Ob[ y ]} {p' : Ob[ p ]} | ||
| {π₁ : Hom p x} {π₂ : Hom p y} | ||
| (prod : is-product B π₁ π₂) | ||
| (π₁' : Hom[ π₁ ] p' x') (π₂' : Hom[ π₂ ] p' y') | ||
| : Type (ob ⊔ ℓb ⊔ oe ⊔ ℓe) | ||
| where | ||
| no-eta-equality | ||
| open is-product prod | ||
| field | ||
| ⟨_,_⟩' | ||
| : ∀ {a a'} {f : Hom a x} {g : Hom a y} | ||
| → (f' : Hom[ f ] a' x') (g' : Hom[ g ] a' y') | ||
| → Hom[ ⟨ f , g ⟩ ] a' p' | ||
| π₁∘⟨⟩' | ||
| : ∀ {a a'} {f : Hom a x} {g : Hom a y} | ||
| → {f' : Hom[ f ] a' x'} {g' : Hom[ g ] a' y'} | ||
| → π₁' ∘' ⟨ f' , g' ⟩' ≡[ π₁∘⟨⟩ ] f' | ||
| π₂∘⟨⟩' | ||
| : ∀ {a a'} {f : Hom a x} {g : Hom a y} | ||
| → {f' : Hom[ f ] a' x'} {g' : Hom[ g ] a' y'} | ||
| → π₂' ∘' ⟨ f' , g' ⟩' ≡[ π₂∘⟨⟩ ] g' | ||
| unique' | ||
| : ∀ {a a'} {f : Hom a x} {g : Hom a y} | ||
| → {f' : Hom[ f ] a' x'} {g' : Hom[ g ] a' y'} | ||
| → {other : Hom a p} {p1 : π₁ ∘ other ≡ f} {p2 : π₂ ∘ other ≡ g} | ||
| → {other' : Hom[ other ] a' p'} | ||
| → (p1' : (π₁' ∘' other') ≡[ p1 ] f') | ||
| → (p2' : (π₂' ∘' other') ≡[ p2 ] g') | ||
| → other' ≡[ unique p1 p2 ] ⟨ f' , g' ⟩' |
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can we clean up these type signatures slightly e.g. using variables, or passing to a parametrised module? that's a lot of code to dump on readers.
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Description
This PR implements total products in displayed categories, as a step towards a nice definition of Hadamard products.
Checklist
Before submitting a merge request, please check the items below:
support/sort-imports.hs(ornix run --experimental-features nix-command -f . sort-imports).If your change affects many files without adding substantial content, and
you don't want your name to appear on those pages (for example, treewide
refactorings or reformattings), start the commit message and PR title with
chore:.