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Symmetric Monoidal Categories #1915

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Apr 24, 2024
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Symmetric Monoidal Categories #1915

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4 changes: 2 additions & 2 deletions theories/WildCat/Bifunctor.v
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Original file line number Diff line number Diff line change
Expand Up @@ -103,14 +103,14 @@ Defined.
Definition fmap10_is_fmap11 {A B C : Type} `{Is1Cat A, Is1Cat B, Is1Cat C}
(F : A -> B -> C) `{!Is0Bifunctor F, !Is1Bifunctor F}
{a0 a1 : A} (f : a0 $-> a1) (b : B)
: fmap11 F f (Id b) $== fmap10 F f b
: fmap11 F f (Id b) $== fmap10 F f b
:= (fmap_id _ _ $@R _) $@ cat_idl _.

(** [fmap11] with left map the identity gives [fmap01]. *)
Definition fmap01_is_fmap11 {A B C : Type} `{Is1Cat A, Is1Cat B, Is1Cat C}
(F : A -> B -> C) `{!Is0Bifunctor F, !Is1Bifunctor F}
(a : A) {b0 b1 : B} (g : b0 $-> b1)
: fmap11 F (Id a) g $== fmap01 F a g
: fmap11 F (Id a) g $== fmap01 F a g
:= (_ $@L fmap_id _ _) $@ cat_idr _.

(** 2-functorial action *)
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5 changes: 3 additions & 2 deletions theories/WildCat/Coproducts.v
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Expand Up @@ -2,7 +2,8 @@ Require Import Basics.Overture Basics.Tactics Basics.Decidable.
Require Import Types.Bool.
Require Import WildCat.Core WildCat.Equiv WildCat.Forall WildCat.NatTrans
WildCat.Opposite WildCat.Products WildCat.Universe
WildCat.Yoneda WildCat.ZeroGroupoid WildCat.PointedCat.
WildCat.Yoneda WildCat.ZeroGroupoid WildCat.PointedCat
WildCat.Monoidal.

(** * Categories with coproducts *)

Expand Down Expand Up @@ -226,7 +227,7 @@ Lemma cate_coprod_assoc {A : Type} `{HasEquivs A}
: cat_bincoprod x (cat_bincoprod y z)
$<~> cat_bincoprod (cat_bincoprod x y) z.
Proof.
exact (@cate_binprod_assoc A^op _ _ _ _ _ e x y z)^-1$.
exact (@associator_binprod A^op _ _ _ _ _ e x y z)^-1$.
Defined.

(** *** Binary coproduct functor *)
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