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Opaque FreeCommAlgebra #1089

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fix FPAlgebra
felixwellen committed Jul 23, 2024
commit 2878b76779945e7febf08a1c0c540103d2dee27d
2 changes: 1 addition & 1 deletion Cubical/Algebra/CommAlgebra/FPAlgebra/Base.agda
Original file line number Diff line number Diff line change
@@ -51,7 +51,7 @@ module _ {R : CommRing ℓ} where
evPolyHomomorphic A B f P values =
(fst f) (evPoly A P values) ≡⟨ refl ⟩
(fst f) (fst (freeInducedHom A values) P) ≡⟨ refl ⟩
fst (f ∘a freeInducedHom A values) P ≡⟨ cong (λ u → fst u P) (natIndHomR f values) ⟩
fst (f ∘a freeInducedHom A values) P ≡⟨ cong (λ u → fst u P) (natIndHomR {A = A} {B = B} f values) ⟩
fst (freeInducedHom B (fst f ∘ values)) P ≡⟨ refl ⟩
evPoly B P (fst f ∘ values) ∎
where open AlgebraHoms
4 changes: 2 additions & 2 deletions Cubical/Algebra/CommAlgebra/FPAlgebra/Instances.agda
Original file line number Diff line number Diff line change
@@ -78,13 +78,13 @@ module _ (R : CommRing ℓ) where
inverse1 : fromA ∘a toA ≡ idAlgebraHom _
inverse1 =
fromA ∘a toA
≡⟨ sym (unique _ _ _ _ _ _ (λ i → cong (fst fromA) (
≡⟨ sym (unique _ _ B _ _ _ (λ i → cong (fst fromA) (
fst toA (generator n emptyGen i)
≡⟨ inducedHomOnGenerators _ _ _ _ _ _ ⟩
Construction.var i
∎))) ⟩
inducedHom n emptyGen B (generator _ _) (relationsHold _ _)
≡⟨ unique _ _ _ _ _ _ (λ i → refl) ⟩
≡⟨ unique _ _ B _ _ _ (λ i → refl) ⟩
idAlgebraHom _
inverse2 : toA ∘a fromA ≡ idAlgebraHom _