Rename the category of relations

This commit is contained in:
Frederik Hanghøj Iversen 2017-11-15 21:51:41 +01:00
parent 6ca9368891
commit 43cc73c6a8

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@ -7,21 +7,6 @@ open import Cubical.GradLemma
open import Agda.Primitive open import Agda.Primitive
open import Category open import Category
-- Sets are built-in to Agda. The set of all small sets is called Set.
Fun : { : Level} ( T U : Set ) Set
Fun T U = T U
𝕊et-as-Cat : { : Level} Category {lsuc } {}
𝕊et-as-Cat {} = record
{ Object = Set
; Arrow = λ T U Fun {} T U
; 𝟙 = λ x x
; _⊕_ = λ g f x g ( f x )
; assoc = refl
; ident = funExt (λ x refl) , funExt (λ x refl)
}
-- Subsets are predicates over some type. -- Subsets are predicates over some type.
Subset : { : Level} ( A : Set ) Set ( lsuc lzero) Subset : { : Level} ( A : Set ) Set ( lsuc lzero)
Subset A = A Set Subset A = A Set
@ -166,8 +151,8 @@ module _ {A B C D : Set} {S : Subset (A × B)} {R : Subset (B × C)} {Q : Subset
(Σ[ b B ] (a , b) S × (Σ[ c C ] (b , c) R × (c , d) Q)) (Σ[ b B ] (a , b) S × (Σ[ c C ] (b , c) R × (c , d) Q))
assocc = equivToPath equi assocc = equivToPath equi
Rel-as-Cat : Category Rel : Category
Rel-as-Cat = record Rel = record
{ Object = Set { Object = Set
; Arrow = λ S R Subset (S × R) ; Arrow = λ S R Subset (S × R)
; 𝟙 = λ {S} Diag S ; 𝟙 = λ {S} Diag S
@ -175,17 +160,3 @@ Rel-as-Cat = record
; assoc = funExt assocc ; assoc = funExt assocc
; ident = funExt ident-l , funExt ident-r ; ident = funExt ident-l , funExt ident-r
} }
module _ { ' : Level} { : Category {} {}} where
private
C-Obj = Object
_+_ = Arrow
RepFunctor : Functor 𝕊et-as-Cat
RepFunctor =
record
{ F = λ A (B : C-Obj) Hom { = } A B
; f = λ { {c' = c'} f g {!HomFromArrow { = } c' g!}}
; ident = {!!}
; distrib = {!!}
}