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Use psquare/phsquare in spectrum

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This commit is contained in:
Yuri Sulyma 2017-06-08 20:01:41 -06:00
parent bc69a96faa
commit aa54adf770
1 changed files with 12 additions and 4 deletions
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16
homotopy/spectrum.hlean
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@ -133,7 +133,12 @@ namespace spectrum
structure smap {N : succ_str} (E F : gen_prespectrum N) := structure smap {N : succ_str} (E F : gen_prespectrum N) :=
(to_fun : Π(n:N), E n →* F n) (to_fun : Π(n:N), E n →* F n)
(glue_square : Π(n:N), glue F n ∘* to_fun n ~* Ω→ (to_fun (S n)) ∘* glue E n) (glue_square : Π(n:N), psquare
(to_fun n)
(Ω→ (to_fun (S n)))
(glue E n)
(glue F n)
)
open smap open smap
infix ` →ₛ `:30 := smap infix ` →ₛ `:30 := smap
@ -180,9 +185,12 @@ namespace spectrum
structure shomotopy {N : succ_str} {E F : gen_prespectrum N} (f g : E →ₛ F) := structure shomotopy {N : succ_str} {E F : gen_prespectrum N} (f g : E →ₛ F) :=
(to_phomotopy : Πn, f n ~* g n) (to_phomotopy : Πn, f n ~* g n)
(glue_homotopy : Πn, pwhisker_left (glue F n) (to_phomotopy n) ⬝* glue_square g n (glue_homotopy : Πn, phsquare
= -- Ideally this should be a "phomotopy2" (pwhisker_left (glue F n) (to_phomotopy n))
glue_square f n ⬝* pwhisker_right (glue E n) (ap1_phomotopy (to_phomotopy (S n)))) (pwhisker_right (glue E n) (ap1_phomotopy (to_phomotopy (S n))))
(glue_square f n)
(glue_square g n)
)
infix ` ~ₛ `:50 := shomotopy infix ` ~ₛ `:50 := shomotopy