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feat(library/hott): complete proof that object types of proper hott categories are one truncated

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Jakob von Raumer 2014-12-03 01:54:05 -05:00 committed by Leonardo de Moura
parent aad4592cad
commit cc2de8a8d9
1 changed files with 6 additions and 8 deletions
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12
library/hott/algebra/category/basic.lean
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@ -2,7 +2,7 @@
-- Released under Apache 2.0 license as described in the file LICENSE. -- Released under Apache 2.0 license as described in the file LICENSE.
-- Author: Jakob von Raumer -- Author: Jakob von Raumer
import ..precategory.basic ..precategory.morphism import ..precategory.basic ..precategory.morphism ..precategory.iso
import hott.equiv hott.trunc import hott.equiv hott.trunc
open precategory morphism is_equiv path truncation nat sigma sigma.ops open precategory morphism is_equiv path truncation nat sigma sigma.ops
@ -24,15 +24,13 @@ namespace category
definition path_of_iso {a b : ob} : a ≅ b → a ≈ b := definition path_of_iso {a b : ob} : a ≅ b → a ≈ b :=
iso_of_path⁻¹ iso_of_path⁻¹
definition foo {a b : ob} : definition ob_1_type : is_trunc nat.zero .+1 ob :=
definition ob_1_type : is_trunc -2 .+1 .+1 .+1 ob :=
begin begin
apply is_trunc_succ, intros (a, b), apply is_trunc_succ, intros (a, b),
/-fapply trunc_equiv, fapply trunc_equiv,
exact (@path_of_iso ob C a b), exact (@path_of_iso _ _ a b),
apply inv_closed, apply inv_closed,
exact sorry,-/ apply is_hset_iso,
end end
end category end category