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squares with two constant maps

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This commit is contained in:
Egbert Rijke 2017-07-01 15:39:25 +01:00
parent 4033195ce3
commit dd18b3a72a
1 changed files with 37 additions and 0 deletions
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37
homotopy/pointed_cubes.hlean
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@ -53,3 +53,40 @@ begin
refine (pwhisker_right ftop psq_right) ⬝* (passoc gbot fright ftop) ⬝* _,
exact (pwhisker_left gbot psq_left),
end
definition psquare_vcompose {A B C D E F : Type*} {ftop : A →* B} {fbot : C →* D} {fleft : A →* C} {fright : B →* D} {gbot : E →* F} {gleft : C →* E} {gright : D →* F} (psq_top : psquare ftop fbot fleft fright) (psq_bot : psquare fbot gbot gleft gright) : psquare ftop gbot (gleft ∘* fleft) (gright ∘* fright) :=
begin
fapply psquare_of_phomotopy,
refine (passoc gright fright ftop) ⬝* _ ⬝* (passoc gbot gleft fleft),
refine (pwhisker_left gright psq_top) ⬝* _,
refine (passoc gright fbot fleft)⁻¹* ⬝* _,
exact pwhisker_right fleft psq_bot,
end
definition psquare_of_pconst_top_bot {A B C D : Type*} (fleft : A →* C) (fright : B →* D) : psquare (pconst A B) (pconst C D) fleft fright :=
begin
fapply psquare_of_phomotopy,
refine (pcompose_pconst fright) ⬝* _,
exact (pconst_pcompose fleft)⁻¹*,
end
definition psquare_of_pconst_left_right {A B C D : Type*} (ftop : A →* B) (fbot : C →* D) : psquare ftop fbot (pconst A C) (pconst B D) :=
begin
fapply psquare_of_phomotopy,
refine (pconst_pcompose ftop) ⬝* _,
exact (pcompose_pconst fbot)⁻¹*
end
definition psquare_of_pconst_top_left {A B C D : Type*} (fbot : C →* D) (fright : B →* D) : psquare (pconst A B) fbot (pconst A C) fright :=
begin
fapply psquare_of_phomotopy,
refine (pcompose_pconst fright) ⬝* _,
exact (pcompose_pconst fbot)⁻¹*,
end
definition psquare_of_pconst_bot_right {A B C D : Type*} (ftop : A →* B) (fleft : A →* C) : psquare ftop (pconst C D) fleft (pconst B D) :=
begin
fapply psquare_of_phomotopy,
refine (pconst_pcompose ftop) ⬝* _,
exact (pconst_pcompose fleft)⁻¹*,
end