diff --git a/homotopy/homology.hlean b/homology/homology.hlean similarity index 85% rename from homotopy/homology.hlean rename to homology/homology.hlean index a0627ec..f5649aa 100644 --- a/homotopy/homology.hlean +++ b/homology/homology.hlean @@ -1,11 +1,12 @@ -import .spectrum .EM ..algebra.arrow_group ..algebra.direct_sum .fwedge ..choice .pushout ..move_to_lib ..algebra.product_group +import ..homotopy.spectrum ..homotopy.EM ..algebra.arrow_group ..algebra.direct_sum ..homotopy.fwedge ..choice ..homotopy.pushout ..move_to_lib open eq spectrum int trunc pointed EM group algebra circle sphere nat EM.ops equiv susp is_trunc - function fwedge cofiber bool lift sigma is_equiv choice pushout algebra unit pi + function fwedge cofiber bool lift sigma is_equiv choice pushout algebra unit pi smash namespace homology /- homology theory -/ + structure homology_theory.{u} : Type.{u+1} := (HH : ℤ → pType.{u} → AbGroup.{u}) (Hh : Π(n : ℤ) {X Y : Type*} (f : X →* Y), HH n X →g HH n Y) diff --git a/homotopy/spectrum.hlean b/homotopy/spectrum.hlean index 3fa2dc4..0cf3cf0 100644 --- a/homotopy/spectrum.hlean +++ b/homotopy/spectrum.hlean @@ -422,8 +422,7 @@ namespace spectrum by induction k with k f; reflexivity; exact f ⬝e* loopn_pequiv_loopn k (equiv_glue X (n +' k)) ⬝e* !loopn_succ_in⁻¹ᵉ* - definition spectrify_map {N : succ_str} {X : gen_prespectrum N} {Y : gen_spectrum N} - (f : X →ₛ Y) : X →ₛ spectrify X := + definition spectrify_map {N : succ_str} {X : gen_prespectrum N} : X →ₛ spectrify X := begin fapply smap.mk, { intro n, exact pinclusion _ 0 },