d2958044fd
After this commit, Lean "cuts" the search after the first instance is
computed. To obtain the previous behavior, we must use the new command
multiple_instances <class-name>
closes #370
40 lines
1.3 KiB
Text
40 lines
1.3 KiB
Text
-- Copyright (c) 2014 Jakob von Raumer. All rights reserved.
|
|
-- Released under Apache 2.0 license as described in the file LICENSE.
|
|
-- Author: Jakob von Raumer
|
|
|
|
import ..precategory.basic ..precategory.morphism ..precategory.iso
|
|
|
|
open precategory morphism is_equiv eq truncation nat sigma sigma.ops
|
|
|
|
-- A category is a precategory extended by a witness,
|
|
-- that the function assigning to each isomorphism a path,
|
|
-- is an equivalecnce.
|
|
structure category [class] (ob : Type) extends (precategory ob) :=
|
|
(iso_of_path_equiv : Π {a b : ob}, is_equiv (@iso_of_path ob (precategory.mk hom _ comp ID assoc id_left id_right) a b))
|
|
|
|
multiple_instances [persistent] category
|
|
|
|
namespace category
|
|
variables {ob : Type} {C : category ob} {a b : ob}
|
|
include C
|
|
|
|
-- Make iso_of_path_equiv a class instance
|
|
-- TODO: Unsafe class instance?
|
|
instance [persistent] iso_of_path_equiv
|
|
|
|
definition path_of_iso {a b : ob} : a ≅ b → a = b :=
|
|
iso_of_path⁻¹
|
|
|
|
definition ob_1_type : is_trunc nat.zero .+1 ob :=
|
|
begin
|
|
apply is_trunc_succ, intros (a, b),
|
|
fapply trunc_equiv,
|
|
exact (@path_of_iso _ _ a b),
|
|
apply inv_closed,
|
|
apply is_hset_iso,
|
|
end
|
|
|
|
end category
|
|
|
|
-- Bundled version of categories
|
|
inductive Category : Type := mk : Π (ob : Type), category ob → Category
|