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simplify shomotopy

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This commit is contained in:
Egbert Rijke 2017-07-01 16:23:50 +01:00
parent ed2ff9f113
commit eed538eb8f
2 changed files with 14 additions and 1 deletions
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6
homotopy/pointed_cubes.hlean
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@ -90,3 +90,9 @@ begin
refine (pconst_pcompose ftop) ⬝* _, refine (pconst_pcompose ftop) ⬝* _,
exact (pconst_pcompose fleft)⁻¹*, exact (pconst_pcompose fleft)⁻¹*,
end end
definition ptube_v {A B C D : Type*} {ftop ftop' : A →* B} (phtpy_top : ftop ~* ftop') {fbot fbot' : C →* D} (phtpy_bot : fbot ~* fbot') {fleft : A →* C} {fright : B →* D} (psq_back : psquare ftop fbot fleft fright) (psq_front : psquare ftop' fbot' fleft fright) : Type :=
phsquare (pwhisker_left fright phtpy_top) (pwhisker_right fleft phtpy_bot) psq_back psq_front
definition ptube_h {A B C D : Type*} {ftop : A →* B} {fbot : C →* D} {fleft fleft' : A →* C} (phtpy_left : fleft ~* fleft') {fright fright' : B →* D} (phtpy_right : fright ~* fright') (psq_back : psquare ftop fbot fleft fright) (psq_front : psquare ftop fbot fleft' fright') : Type :=
phsquare (pwhisker_right ftop phtpy_right) (pwhisker_left fbot phtpy_left) psq_back psq_front

9
homotopy/spectrum.hlean
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@ -201,11 +201,18 @@ 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, phsquare (glue_homotopy : Πn, ptube_v
(to_phomotopy n)
(ap1_phomotopy (to_phomotopy (S n)))
(glue_square f n)
(glue_square g n))
/- (glue_homotopy : Πn, phsquare
(pwhisker_left (glue F n) (to_phomotopy n)) (pwhisker_left (glue F n) (to_phomotopy 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 f n)
(glue_square g n)) (glue_square g n))
-/
infix ` ~ₛ `:50 := shomotopy infix ` ~ₛ `:50 := shomotopy