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start map from spectrum to its truncation

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Ulrik Buchholtz 2017-06-28 23:02:09 +01:00
parent 55b831d713
commit 79d13fd0d2
1 changed files with 8 additions and 0 deletions
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8
homotopy/strunc.hlean
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@ -32,6 +32,10 @@ end
-- NB the carrier of ptrunc_int k X is not definitionally -- NB the carrier of ptrunc_int k X is not definitionally
-- equal to trunc_int k (carrier X) -- equal to trunc_int k (carrier X)
definition ptr_int (k : ℤ) (X : pType) : X →* ptrunc_int k X :=
pmap.mk (λ x, int.cases_on k (λ k', tr x) (λ k', up star))
(int.cases_on k (λ k', idp) (λ k', idp))
definition ptrunc_int_pequiv_ptrunc_int (k : ℤ) {X Y : Type*} (e : X ≃* Y) : definition ptrunc_int_pequiv_ptrunc_int (k : ℤ) {X Y : Type*} (e : X ≃* Y) :
ptrunc_int k X ≃* ptrunc_int k Y := ptrunc_int k X ≃* ptrunc_int k Y :=
begin begin
@ -167,4 +171,8 @@ have I : m < 2, from
(is_trunc_of_is_trunc_int m (E (2 - k)) (K (2 - k))) (is_trunc_of_is_trunc_int m (E (2 - k)) (K (2 - k)))
(nat.succ_le_succ (max0_le_of_le (le_sub_one_of_lt I))) (nat.succ_le_succ (max0_le_of_le (le_sub_one_of_lt I)))
definition str [constructor] (k : ℤ) (E : spectrum) : E →ₛ strunc k E :=
smap.mk (λ n, ptr_int (k + n) (E n))
sorry
end spectrum end spectrum