4f2e0c6d7f
The new command provides a uniform way to set declaration attributes. It replaces the commands: class, instance, coercion, multiple_instances, reducible, irreducible
21 lines
734 B
Text
21 lines
734 B
Text
prelude
|
|
-- category
|
|
|
|
definition Prop := Type.{0}
|
|
constant eq {A : Type} : A → A → Prop
|
|
infix `=`:50 := eq
|
|
|
|
inductive category (ob : Type) (mor : ob → ob → Type) : Type :=
|
|
mk : Π (id : Π (A : ob), mor A A),
|
|
(Π (A B : ob) (f : mor A A), id A = f) → category ob mor
|
|
|
|
definition id (ob : Type) (mor : ob → ob → Type) (Cat : category ob mor) := category.rec (λ id idl, id) Cat
|
|
|
|
attribute id [reducible]
|
|
theorem id_left (ob : Type) (mor : ob → ob → Type) (Cat : category ob mor) (A : ob) (f : mor A A) :
|
|
@eq (mor A A) (id ob mor Cat A) f :=
|
|
@category.rec ob mor (λ (C : category ob mor), @eq (mor A A) (id ob mor C A) f)
|
|
(λ (id : Π (A : ob), mor A A)
|
|
(idl : Π (A : ob), _),
|
|
idl A A f)
|
|
Cat
|