order of arguments in group.mk has changed

This commit is contained in:
Floris van Doorn 2017-02-02 17:14:48 -05:00
parent d6de922d1f
commit c0b7740f13
9 changed files with 36 additions and 16 deletions

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@ -8,8 +8,8 @@ namespace group
definition group_arrow [instance] (A B : Type) [group B] : group (A → B) := definition group_arrow [instance] (A B : Type) [group B] : group (A → B) :=
begin begin
fapply group.mk, fapply group.mk,
{ intro f g a, exact f a * g a },
{ apply is_trunc_arrow }, { apply is_trunc_arrow },
{ intro f g a, exact f a * g a },
{ intros, apply eq_of_homotopy, intro a, apply mul.assoc }, { intros, apply eq_of_homotopy, intro a, apply mul.assoc },
{ intro a, exact 1 }, { intro a, exact 1 },
{ intros, apply eq_of_homotopy, intro a, apply one_mul }, { intros, apply eq_of_homotopy, intro a, apply one_mul },
@ -31,9 +31,9 @@ namespace group
definition pgroup_ppmap [instance] (A B : Type*) [pgroup B] : pgroup (ppmap A B) := definition pgroup_ppmap [instance] (A B : Type*) [pgroup B] : pgroup (ppmap A B) :=
begin begin
fapply pgroup.mk, fapply pgroup.mk,
{ apply is_trunc_pmap },
{ intro f g, apply pmap.mk (λa, f a * g a), { intro f g, apply pmap.mk (λa, f a * g a),
exact ap011 mul (respect_pt f) (respect_pt g) ⬝ !one_mul }, exact ap011 mul (respect_pt f) (respect_pt g) ⬝ !one_mul },
{ apply is_trunc_pmap },
{ intros, apply pmap_eq_of_homotopy, intro a, apply mul.assoc }, { intros, apply pmap_eq_of_homotopy, intro a, apply mul.assoc },
{ intro f, apply pmap.mk (λa, (f a)⁻¹), apply inv_eq_one, apply respect_pt }, { intro f, apply pmap.mk (λa, (f a)⁻¹), apply inv_eq_one, apply respect_pt },
{ intros, apply pmap_eq_of_homotopy, intro a, apply one_mul }, { intros, apply pmap_eq_of_homotopy, intro a, apply one_mul },

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@ -137,7 +137,7 @@ namespace group
variables (X) variables (X)
definition group_free_ab_group [constructor] : ab_group (fcg_carrier X) := definition group_free_ab_group [constructor] : ab_group (fcg_carrier X) :=
ab_group.mk fcg_mul _ fcg_mul_assoc fcg_one fcg_one_mul fcg_mul_one ab_group.mk _ fcg_mul fcg_mul_assoc fcg_one fcg_one_mul fcg_mul_one
fcg_inv fcg_mul_left_inv fcg_mul_comm fcg_inv fcg_mul_left_inv fcg_mul_comm
definition free_ab_group [constructor] : AbGroup := definition free_ab_group [constructor] : AbGroup :=

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@ -112,8 +112,8 @@ namespace group
-- export [reduce_hints] free_group -- export [reduce_hints] free_group
variables (X) variables (X)
definition group_free_group [constructor] : group (free_group_carrier X) := definition group_free_group [constructor] : group (free_group_carrier X) :=
group.mk free_group_mul _ free_group_mul_assoc free_group_one free_group_one_mul free_group_mul_one group.mk _ free_group_mul free_group_mul_assoc free_group_one free_group_one_mul
free_group_inv free_group_mul_left_inv free_group_mul_one free_group_inv free_group_mul_left_inv
definition free_group [constructor] : Group := definition free_group [constructor] : Group :=
Group.mk _ (group_free_group X) Group.mk _ (group_free_group X)

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@ -46,7 +46,7 @@ namespace group
variables (G G') variables (G G')
definition group_prod [constructor] : group (G × G') := definition group_prod [constructor] : group (G × G') :=
group.mk product_mul _ product_mul_assoc product_one product_one_mul product_mul_one group.mk _ product_mul product_mul_assoc product_one product_one_mul product_mul_one
product_inv product_mul_left_inv product_inv product_mul_left_inv
definition product [constructor] : Group := definition product [constructor] : Group :=

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@ -125,7 +125,7 @@ namespace group
variable (N) variable (N)
definition group_qg [constructor] : group (qg N) := definition group_qg [constructor] : group (qg N) :=
group.mk quotient_mul _ quotient_mul_assoc quotient_one quotient_one_mul quotient_mul_one group.mk _ quotient_mul quotient_mul_assoc quotient_one quotient_one_mul quotient_mul_one
quotient_inv quotient_mul_left_inv quotient_inv quotient_mul_left_inv
definition quotient_group [constructor] : Group := definition quotient_group [constructor] : Group :=

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@ -214,7 +214,7 @@ namespace group
variable (H) variable (H)
definition group_sg [constructor] : group (sg H) := definition group_sg [constructor] : group (sg H) :=
group.mk subgroup_mul _ subgroup_mul_assoc subgroup_one subgroup_one_mul subgroup_mul_one group.mk _ subgroup_mul subgroup_mul_assoc subgroup_one subgroup_one_mul subgroup_mul_one
subgroup_inv subgroup_mul_left_inv subgroup_inv subgroup_mul_left_inv
definition subgroup [constructor] : Group := definition subgroup [constructor] : Group :=

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@ -188,12 +188,12 @@ namespace seq_colim
seq_diagram (λn, Πx, A x n) := seq_diagram (λn, Πx, A x n) :=
λn f x, g (f x) λn f x, g (f x)
namespace seq_colim.ops namespace ops
abbreviation ι [constructor] := @inclusion abbreviation ι [constructor] := @inclusion
abbreviation pι [constructor] {A} (f) {n} := @pinclusion A f n abbreviation pι [constructor] {A} (f) {n} := @pinclusion A f n
abbreviation pι' [constructor] [parsing_only] := @pinclusion abbreviation pι' [constructor] [parsing_only] := @pinclusion
abbreviation ι' [constructor] [parsing_only] {A} (f n) := @inclusion A f n abbreviation ι' [constructor] [parsing_only] {A} (f n) := @inclusion A f n
end seq_colim.ops end ops
open seq_colim.ops open seq_colim.ops
definition rep0_glue (k : ) (a : A 0) : ι f (rep0 f k a) = ι f a := definition rep0_glue (k : ) (a : A 0) : ι f (rep0 f k a) = ι f a :=

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@ -8,7 +8,9 @@ Reduced cohomology
import algebra.arrow_group .spectrum homotopy.EM import algebra.arrow_group .spectrum homotopy.EM
open eq spectrum int trunc pointed EM group algebra circle sphere nat EM.ops open eq spectrum int trunc pointed EM group algebra circle sphere nat EM.ops equiv susp
namespace cohomology
definition EM_spectrum /-[constructor]-/ (G : AbGroup) : spectrum := definition EM_spectrum /-[constructor]-/ (G : AbGroup) : spectrum :=
spectrum.Mk (K G) (λn, (loop_EM G n)⁻¹ᵉ*) spectrum.Mk (K G) (λn, (loop_EM G n)⁻¹ᵉ*)
@ -43,3 +45,21 @@ definition cohomology_homomorphism_compose {X X' X'' : Type*} (g : X'' →* X')
(Y : spectrum) (n : ) (h : H^n[X, Y]) : cohomology_homomorphism (f ∘* g) Y n h ~* (Y : spectrum) (n : ) (h : H^n[X, Y]) : cohomology_homomorphism (f ∘* g) Y n h ~*
cohomology_homomorphism g Y n (cohomology_homomorphism f Y n h) := cohomology_homomorphism g Y n (cohomology_homomorphism f Y n h) :=
!passoc⁻¹* !passoc⁻¹*
end cohomology
exit
definition cohomology_psusp (X : Type*) (Y : spectrum) (n : ) :
H^n+1[psusp X, Y] ≃ H^n[X, Y] :=
calc
H^n+1[psusp X, Y] ≃ psusp X →* πg[2] (Y (2+(n+1))) : by reflexivity
... ≃ X →* Ω (πg[2] (Y (2+(n+1)))) : psusp_adjoint_loop_unpointed
-- ... ≃ X →* πg[3] (Y (2+(n+1))) : _
--... ≃ X →* πag[3] (Y ((2+n)+1)) : _
... ≃ X →* πg[2] (Y (2+n)) :
begin
refine equiv_of_pequiv (pequiv_ppcompose_left _),
refine !homotopy_group_succ_o ⬝ _,
exact sorry --refine _ ⬝e* _ ⬝e* _
end
... ≃ H^n[X, Y] : by reflexivity

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@ -858,8 +858,8 @@ namespace category
begin begin
have foo : Π(g : A), @inv A G g = (@inv A G g * g) * @inv A H g, have foo : Π(g : A), @inv A G g = (@inv A G g * g) * @inv A H g,
from λg, !mul_inv_cancel_right⁻¹, from λg, !mul_inv_cancel_right⁻¹,
cases G with Gm Gs Gh1 G1 Gh2 Gh3 Gi Gh4, cases G with Gs Gm Gh1 G1 Gh2 Gh3 Gi Gh4,
cases H with Hm Hs Hh1 H1 Hh2 Hh3 Hi Hh4, cases H with Hs Hm Hh1 H1 Hh2 Hh3 Hi Hh4,
change Gi ~ Hi, intro g, have p' : Gm ~2 Hm, from p, change Gi ~ Hi, intro g, have p' : Gm ~2 Hm, from p,
calc calc
Gi g = Hm (Hm (Gi g) g) (Hi g) : foo Gi g = Hm (Hm (Gi g) g) (Hi g) : foo
@ -910,9 +910,9 @@ namespace category
induction G with G g, induction H with H h, induction G with G g, induction H with H h,
esimp [Group.sigma_char2] at p, induction p, esimp [Group.sigma_char2] at p, induction p,
refine !pathover_idp ⬝e _, refine !pathover_idp ⬝e _,
induction g with m s ma o om mo i mi, induction h with μ σ μa ε εμ με ι μι, induction g with s m ma o om mo i mi, induction h with σ μ μa ε εμ με ι μι,
exact Group_eq_equiv_lemma2 (Group.sigma_char2 (Group.mk G (group.mk m s ma o om mo i mi))).2.2 exact Group_eq_equiv_lemma2 (Group.sigma_char2 (Group.mk G (group.mk s m ma o om mo i mi))).2.2
(Group.sigma_char2 (Group.mk G (group.mk μ σ μa ε εμ με ι μι))).2.2 (Group.sigma_char2 (Group.mk G (group.mk σ μ μa ε εμ με ι μι))).2.2
end end
definition isomorphism.sigma_char (G H : Group) : (G ≃g H) ≃ Σ(e : G ≃ H), is_mul_hom e := definition isomorphism.sigma_char (G H : Group) : (G ≃g H) ≃ Σ(e : G ≃ H), is_mul_hom e :=