Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
for the purposes of having direct links to it, I gave a side-remark at stable Dold-Kan correspondence its own page: rational stable homotopy theory, recording the equivalence
(Hℚ)ModSpectra≃Ch•(ℚ)I also added the claim that under this identification and that of classical rational homotopy theory then the derived version of the free-forgetful adjunction
(dgcAlg≥2ℚ)/ℚ[0]Sym∘cn⟵⊥⟶U∘ker(ε(−))Ch•(ℚ)models the stabilization adjunction (Σ∞⊣Ω∞). But I haven’t type the proof into the entry yet.
I have added to the beginning of the entry (rational stable homotopy theory) a remark that rational spectra are Hℚ-module spectra. Deserves to be further expanded.
In #1 I wrote:
I also added the claim that [...] But I haven’t type the proof into the entry yet.
Done now, here:
The following composite total derived functors
Ho(Spectraℚ,fin)↓≃↑Ho(Chℚ,•,fin)𝕃i2⟵⊥⟶ℝcn2Ho(Chℚ,>1,fin)↓≃↑(−)*Ho(Ch>1ℚ,fin)op(ℝ(U∘ker(ε(−))))op⟵⊥⟶(𝕃Sym/ℚ[0])opHo(dgcAlg>0ℚ,fin)/ℚ[0])op↕≃Ho(Topℚ,>1,fin)agree with the restriction of the stabilization infinity-adjunction
SpectraΣ∞⟵⊥⟶Ω∞∞Grpd*/to simply connected rational homotopy types of finite type.
1 to 3 of 3