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authorJacques Comeaux <jacquesrcomeaux@protonmail.com>2026-09-03 19:22:21 -0500
committerJacques Comeaux <jacquesrcomeaux@protonmail.com>2026-09-03 19:22:21 -0500
commit4e6acbf8b8084bea12327683aceb300a9b64c367 (patch)
tree18ce77db537b4fdd7ef5be66b09a84ea22195f10 /Object
parent42ab1c0b0fc5e7f16123b628dc65a38274d22f3d (diff)
Add Frobenius monoids and hypergraph categoriesmain
Diffstat (limited to 'Object')
-rw-r--r--Object/Monoid/Frobenius.agda40
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+{-# OPTIONS --without-K --safe #-}
+
+open import Categories.Category using (Category)
+open import Categories.Category.Monoidal using (Monoidal)
+open import Categories.Category.Monoidal.Symmetric using (Symmetric)
+open import Level using (Level; _⊔_)
+
+module Object.Monoid.Frobenius {o ℓ e : Level} {C : Category o ℓ e} {M : Monoidal C} (S : Symmetric M) where
+
+open import Categories.Category.Monoidal.Symmetric.Properties S using () renaming (symmetric-Op to Sᵒᵖ)
+open import Object.Monoid.Commutative using (IsCommutativeMonoid)
+
+open Category C
+
+record IsSpecialCommutativeFrobeniusMonoid (A : Obj) : Set (ℓ ⊔ e) where
+
+ field
+ commutativeMonoid : IsCommutativeMonoid S A
+ cocommutativeComonoid : IsCommutativeMonoid Sᵒᵖ A
+
+ open IsCommutativeMonoid commutativeMonoid
+ using (μ; η; commutative)
+ renaming (assoc to μ-assoc; identityˡ to μ-η-identityˡ; identityʳ to μ-η-identityʳ)
+ public
+
+ open IsCommutativeMonoid cocommutativeComonoid
+ using ()
+ renaming (μ to δ; η to ϵ; assoc to δ-assoc; identityˡ to δ-ϵ-identityˡ; identityʳ to δ-ϵ-identityʳ; commutative to cocommutative)
+ public
+
+ field
+ special : μ ∘ δ ≈ id
+
+record SpecialCommutativeFrobeniusMonoid : Set (o ⊔ ℓ ⊔ e) where
+
+ field
+ Carrier : Obj
+ isSpecialCommutativeFrobeniusMonoid : IsSpecialCommutativeFrobeniusMonoid Carrier
+
+ open IsSpecialCommutativeFrobeniusMonoid isSpecialCommutativeFrobeniusMonoid public