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add functoriality of gloopn'

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Floris van Doorn 2018-09-24 17:29:16 +02:00
parent f2dfca25f9
commit 070d687c7f
1 changed files with 5 additions and 0 deletions
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hott/algebra/inf_group_theory.hlean
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@ -374,8 +374,13 @@ namespace group
definition gapn (n : ℕ) [H : is_succ n] {A B : Type*} (f : A →* B) : Ωg[n] A →∞g Ωg[n] B := definition gapn (n : ℕ) [H : is_succ n] {A B : Type*} (f : A →* B) : Ωg[n] A →∞g Ωg[n] B :=
inf_homomorphism.mk (Ω→[n] f) (by induction H with n; exact apn_con n f) inf_homomorphism.mk (Ω→[n] f) (by induction H with n; exact apn_con n f)
definition gapn' (n : ℕ) {A B : InfGroup} (f : A →∞g B) : Ωg'[n] A →∞g Ωg'[n] B :=
inf_homomorphism.mk (Ω→[n] (pmap_of_inf_homomorphism f))
(by cases n with n; exact inf_homomorphism.struct f; exact apn_con n (pmap_of_inf_homomorphism f))
notation `Ωg→` := gap1 notation `Ωg→` := gap1
notation `Ωg→[`:95 n:0 `]`:0 := gapn n notation `Ωg→[`:95 n:0 `]`:0 := gapn n
notation `Ωg'→[`:95 n:0 `]`:0 := gapn' n
definition gloop_isomorphism_gloop {A B : Type*} (f : A ≃* B) : Ωg A ≃∞g Ωg B := definition gloop_isomorphism_gloop {A B : Type*} (f : A ≃* B) : Ωg A ≃∞g Ωg B :=
inf_isomorphism.mk (Ωg→ f) (to_is_equiv (loop_pequiv_loop f)) inf_isomorphism.mk (Ωg→ f) (to_is_equiv (loop_pequiv_loop f))