CategoryTheory/agda-kleisli
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Leon Vatthauer 2023-07-15 12:29:26 +02:00
parent f2cccdbdf0
commit c521bf635a
Signed by: leonv
SSH key fingerprint: SHA256:G4+ddwoZmhLPRB1agvXzZMXIzkVJ36dUYZXf5NxT+u8
1 changed files with 12 additions and 7 deletions
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ExtensionSystem.agda
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@ -32,8 +32,11 @@ ExtensionSystem→Monad {𝒞 = 𝒞} 𝐾 = record
{ F = T { F = T
; η = η' ; η = η'
; μ = μ' ; μ = μ'
-- M3
; identityˡ = Identityˡ ; identityˡ = Identityˡ
-- M2
; identityʳ = K2 ; identityʳ = K2
-- M1
; assoc = assoc' ; assoc = assoc'
; sym-assoc = sym assoc' ; sym-assoc = sym assoc'
} }
@ -45,10 +48,12 @@ ExtensionSystem→Monad {𝒞 = 𝒞} 𝐾 = record
T = RMonad⇒Functor 𝐾 T = RMonad⇒Functor 𝐾
open Functor T renaming (F₁ to T₁) open Functor T renaming (F₁ to T₁)
open Equiv open Equiv
-- constructing the natural transformation η from the given family of morphisms 'unit'
η' = ntHelper {F = Id} {G = T} record η' = ntHelper {F = Id} {G = T} record
{ η = λ X → unit { η = λ X → unit
; commute = λ {X} {Y} f → sym K2 ; commute = λ {X} {Y} f → sym K2
} }
-- constructing the natural transformation μ
μ' = ntHelper {F = T ∘F T} {G = T} record μ' = ntHelper {F = T ∘F T} {G = T} record
{ η = λ X → (idC {A = T₀ X})ᵀ { η = λ X → (idC {A = T₀ X})ᵀ
; commute = λ {X} {Y} f → begin ; commute = λ {X} {Y} f → begin