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higher groups: add is_trunc_ppi_of_is_conn

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Floris van Doorn 2018-02-01 00:10:58 -05:00
parent 2f957b7828
commit cf25666beb
1 changed files with 9 additions and 3 deletions
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higher_groups.hlean
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@ -17,13 +17,19 @@ universe variable u
the higher group paper -/ the higher group paper -/
namespace hide namespace hide
open pushout open pushout
definition connect_intro_pequiv {k : ℕ} {X : Type*} (Y : Type*) (H : is_conn k X) : definition connect_intro_pequiv {k : ℕ} {B : Type*} (A : Type*) (H : is_conn k B) :
ppmap X (connect k Y) ≃* ppmap X Y := ppmap B (connect k A) ≃* ppmap B A :=
is_conn.connect_intro_pequiv Y H is_conn.connect_intro_pequiv A H
definition is_conn_fun_prod_of_wedge (n m : ℕ) (A B : Type*) definition is_conn_fun_prod_of_wedge (n m : ℕ) (A B : Type*)
[cA : is_conn n A] [cB : is_conn m B] : is_conn_fun (m + n) (@prod_of_wedge A B) := [cA : is_conn n A] [cB : is_conn m B] : is_conn_fun (m + n) (@prod_of_wedge A B) :=
is_conn_fun_prod_of_wedge n m A B is_conn_fun_prod_of_wedge n m A B
definition is_trunc_ppi_of_is_conn (k n : ℕ) (X : Type*) (H : is_conn (k.-1) X)
(Y : X → Type*) (H3 : Πx, is_trunc (k + n) (Y x)) :
is_trunc n (Π*(x : X), Y x) :=
is_conn.is_trunc_ppi_of_is_conn _ (k.-2) _ _ (le_of_eq (sub_one_add_plus_two_sub_one k n)⁻¹) _ H3
end hide end hide
/- The k-groupal n-types. /- The k-groupal n-types.