23 lines
935 B
Text
23 lines
935 B
Text
inductive [class] category (ob : Type) (mor : ob → ob → Type) : Type
|
|
| mk : Π (comp : Π⦃A B C : ob⦄, mor B C → mor A B → mor A C)
|
|
(id : Π {A : ob}, mor A A),
|
|
(Π {A B C D : ob} {f : mor A B} {g : mor B C} {h : mor C D},
|
|
comp h (comp g f) = comp (comp h g) f) →
|
|
(Π {A B : ob} {f : mor A B}, comp f id = f) →
|
|
(Π {A B : ob} {f : mor A B}, comp id f = f) →
|
|
category
|
|
|
|
namespace category
|
|
section sec_cat
|
|
parameter A : Type
|
|
inductive [class] foo
|
|
| mk : A → foo
|
|
|
|
parameters {ob : Type} {mor : ob → ob → Type} {Cat : category ob mor}
|
|
definition compose := category.rec (λ comp id assoc idr idl, comp) Cat
|
|
definition id := category.rec (λ comp id assoc idr idl, id) Cat
|
|
local infixr ∘ := compose
|
|
inductive is_section {A B : ob} (f : mor A B) : Type
|
|
| mk : ∀g : mor B A, g ∘ f = id → is_section
|
|
end sec_cat
|
|
end category
|