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-rw-r--r--Category/Cocomplete/Finitely/Product.agda20
-rw-r--r--Category/Cocomplete/Finitely/SymmetricMonoidal.agda4
2 files changed, 11 insertions, 13 deletions
diff --git a/Category/Cocomplete/Finitely/Product.agda b/Category/Cocomplete/Finitely/Product.agda
index 25dc346..4b74171 100644
--- a/Category/Cocomplete/Finitely/Product.agda
+++ b/Category/Cocomplete/Finitely/Product.agda
@@ -6,20 +6,21 @@ open import Level using (Level)
module Category.Cocomplete.Finitely.Product {o β„“ e : Level} {π’ž π’Ÿ : Category o β„“ e} where
open import Categories.Category using (_[_,_])
+open import Categories.Category.BinaryCoproducts using (BinaryCoproducts)
+open import Categories.Category.Cocartesian using (Cocartesian)
open import Categories.Category.Cocomplete.Finitely using (FinitelyCocomplete)
-open import Categories.Category.Cocartesian using (Cocartesian; BinaryCoproducts)
open import Categories.Category.Product using (Product)
open import Categories.Diagram.Coequalizer using (Coequalizer)
open import Categories.Object.Coproduct using (Coproduct)
open import Categories.Object.Initial using (IsInitial; Initial)
-open import Data.Product.Base using (_,_; _Γ—_; dmap; zip; map)
+open import Data.Product using (_,_; _Γ—_; dmap; zip; map)
Initial-Γ— : Initial π’ž β†’ Initial π’Ÿ β†’ Initial (Product π’žΒ π’Ÿ)
Initial-Γ— initial-π’ž initial-π’Ÿ = record
{ βŠ₯ = π’ž.βŠ₯ , π’Ÿ.βŠ₯
; βŠ₯-is-initial = record
- { ! = π’ž.! , π’Ÿ.!
- ; !-unique = dmap π’ž.!-unique π’Ÿ.!-unique
+ { Β‘ = π’ž.Β‘ , π’Ÿ.Β‘
+ ; Β‘-unique = dmap π’ž.Β‘-unique π’Ÿ.Β‘-unique
}
}
where
@@ -31,20 +32,17 @@ Coproducts-Γ— coproducts-π’ž coproducts-π’Ÿ = record { coproduct = coproduct }
where
coproduct : βˆ€ {(A₁ , B₁) (Aβ‚‚ , Bβ‚‚) : _ Γ— _} β†’ Coproduct (Product π’ž π’Ÿ) (A₁ , B₁) (Aβ‚‚ , Bβ‚‚)
coproduct = record
- { A+B = π’ž.A+B , π’Ÿ.A+B
+ { A+B = _ π’ž.+ _ , _ π’Ÿ.+ _
; i₁ = π’ž.i₁ , π’Ÿ.i₁
; iβ‚‚ = π’ž.iβ‚‚ , π’Ÿ.iβ‚‚
; [_,_] = zip π’ž.[_,_] π’Ÿ.[_,_]
; inject₁ = π’ž.inject₁ , π’Ÿ.inject₁
; injectβ‚‚ = π’ž.injectβ‚‚ , π’Ÿ.injectβ‚‚
- ; unique = zip π’ž.unique π’Ÿ.unique
+ ; unique = zip π’ž.+-unique π’Ÿ.+-unique
}
where
- module Coprod {π’ž} (coprods : BinaryCoproducts π’ž) where
- open BinaryCoproducts coprods using (coproduct)
- open coproduct public
- module π’ž = Coprod coproducts-π’ž
- module π’Ÿ = Coprod coproducts-π’Ÿ
+ module π’ž = BinaryCoproducts coproducts-π’ž
+ module π’Ÿ = BinaryCoproducts coproducts-π’Ÿ
Coequalizer-Γ—
: (βˆ€ {A} {B} (f g : π’ž [ A , B ]) β†’ Coequalizer π’ž f g)
diff --git a/Category/Cocomplete/Finitely/SymmetricMonoidal.agda b/Category/Cocomplete/Finitely/SymmetricMonoidal.agda
index 2b66d19..bae9774 100644
--- a/Category/Cocomplete/Finitely/SymmetricMonoidal.agda
+++ b/Category/Cocomplete/Finitely/SymmetricMonoidal.agda
@@ -5,8 +5,8 @@ open import Categories.Category.Core using (Category)
module Category.Cocomplete.Finitely.SymmetricMonoidal {o β„“ e} {π’ž : Category o β„“ e} where
open import Categories.Category.Cocomplete.Finitely π’ž using (FinitelyCocomplete)
-open import Categories.Category.Cocartesian π’ž using (module CocartesianMonoidal; module CocartesianSymmetricMonoidal)
-
+open import Categories.Category.Cocartesian.Monoidal using (module CocartesianMonoidal)
+open import Categories.Category.Cocartesian.SymmetricMonoidal π’ž using (module CocartesianSymmetricMonoidal)
module FinitelyCocompleteSymmetricMonoidal (finCo : FinitelyCocomplete) where