2017-05-25 17:46:35 +00:00
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- reindex spheres
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- define pmap in terms of ppi
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- move move_to_lib and pointed to library
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2017-06-02 16:15:31 +00:00
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talk with Favonia about:
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- dependent pointed maps
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- higher cube filling strategies
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- HIT equivalences
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- algebra
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2017-06-05 21:09:48 +00:00
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/-
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Adjointness:
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Σ X ⟶ Y X ∧ Y → Z
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======= ===========
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X → Ω Y X → (Y → Z)
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Spectrum: Y : ℕ → Type* with e : Ω Yₙ₊₁ ≃* Yₙ.
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HOMOLOGY:
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Hₙ(X, Y) :≡? ∥ X ∧ Ω² (Y (n+2)) ∥₀ ≃ ∥ X ∧ Y n ∥₀
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Eilenberg Steenrod-axioms:
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H : ℤ → Type* → AbGroup
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- functorial in second argument
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- (optional): respects pointed equivalences and pointed homotopies
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axioms:
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- the canonical map
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-
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- Given (Xᵢ)ᵢ : I → Type* (satisfying AC?) the canonical functor
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⊕ hₙ
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-/
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