This commit is contained in:
Frederik Hanghøj Iversen 2018-01-21 15:19:15 +01:00
parent ea3e14af96
commit b158b1d420

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@ -22,25 +22,24 @@ record Functor {c c' d d'} (C : Category c c') (D : Category
func→ (a' C.⊕ a) func→ a' D.⊕ func→ a
module _ { ' : Level} {A B C : Category '} (F : Functor B C) (G : Functor A B) where
open Functor
open Category
private
open module F = Functor F
open module G = Functor G
open module A = Category A
open module B = Category B
open module C = Category C
F* = F .func*
F→ = F .func→
G* = G .func*
G→ = G .func→
_A⊕_ = A ._⊕_
_B⊕_ = B ._⊕_
_C⊕_ = C ._⊕_
module _ {a0 a1 a2 : A .Object} {α0 : A .Arrow a0 a1} {α1 : A .Arrow a1 a2} where
dist : (F→ G→) (α1 A.⊕ α0) (F→ G→) α1 C.⊕ (F→ G→) α0
dist : (F→ G→) (α1 A⊕ α0) (F→ G→) α1 C⊕ (F→ G→) α0
dist = begin
(F→ G→) (α1 A. α0) ≡⟨ refl
F→ (G→ (α1 A. α0)) ≡⟨ cong F→ G.distrib
F→ ((G→ α1) B. (G→ α0)) ≡⟨ F.distrib
(F→ G→) α1 C. (F→ G→) α0
(F→ G→) (α1 A⊕ α0) ≡⟨ refl
F→ (G→ (α1 A⊕ α0)) ≡⟨ cong F→ (G .distrib)
F→ ((G→ α1) B⊕ (G→ α0)) ≡⟨ F .distrib
(F→ G→) α1 C⊕ (F→ G→) α0
functor-comp : Functor A C
functor-comp =
@ -49,7 +48,7 @@ module _ { ' : Level} {A B C : Category '} (F : Functor B C) (G : F
; func→ = F→ G→
; ident = begin
(F→ G→) (A .𝟙) ≡⟨ refl
F→ (G→ (A.𝟙)) ≡⟨ cong F→ G.ident
F→ (G→ (A .𝟙)) ≡⟨ cong F→ (G .ident)
F→ (B .𝟙) ≡⟨ F .ident
C .𝟙
; distrib = dist