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Define multicategories #1278

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76170be
Define multicategories
anshwad10 Nov 24, 2025
d4e166b
Update Base.agda
anshwad10 Nov 25, 2025
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3 changes: 3 additions & 0 deletions Cubical/Categories/Multicategories.agda
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module Cubical.Categories.Multicategories where

open import Cubical.Categories.Multicategories.Base
19 changes: 19 additions & 0 deletions Cubical/Categories/Multicategories/Base.agda
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open import Cubical.Foundations.Prelude

open import Cubical.WildCat.Functor
open import Cubical.WildCat.Monad
open import Cubical.WildCat.Instances.Types

module Cubical.Categories.Multicategories.Base ℓ (T : WildMonad (TypeCat ℓ)) where

open WildFunctor (T .fst) renaming (F-ob to T-ob; F-hom to T-hom; F-id to T-id; F-seq to T-seq)
open IsMonad (T .snd)
open WildNatTrans η renaming (N-ob to η-ob; N-hom to η-hom)
open WildNatTrans μ renaming (N-ob to μ-ob; N-hom to μ-hom)

record Multicategory ℓ' : Type (ℓ-suc (ℓ-max ℓ ℓ')) where
no-eta-equality
field
Ob : Type ℓ
Hom : T-ob Ob → Ob → Type ℓ'
id : ∀ {x} → Hom (η-ob _ x) x