- reindex spheres - define pmap in terms of ppi - move move_to_lib and pointed to library talk with Favonia about: - dependent pointed maps - higher cube filling strategies - HIT equivalences - algebra /- Adjointness: Σ X ⟶ Y X ∧ Y → Z ======= =========== X → Ω Y X → (Y → Z) Spectrum: Y : ℕ → Type* with e : Ω Yₙ₊₁ ≃* Yₙ. HOMOLOGY: Hₙ(X, Y) :≡? ∥ X ∧ Ω² (Y (n+2)) ∥₀ ≃ ∥ X ∧ Y n ∥₀ Eilenberg Steenrod-axioms: H : ℤ → Type* → AbGroup - functorial in second argument - (optional): respects pointed equivalences and pointed homotopies axioms: - the canonical map - - Given (Xᵢ)ᵢ : I → Type* (satisfying AC?) the canonical functor ⊕ hₙ -/