43 lines
2.3 KiB
Text
43 lines
2.3 KiB
Text
-- WIP
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import ..move_to_lib
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open function eq
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namespace pushout
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section
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-- structure span2 : Type :=
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-- {A₀₀ A₀₂ A₀₄ A₂₀ A₂₂ A₂₄ A₄₀ A₄₂ A₄₄ : Type}
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-- {f₀₁ : A₀₂ → A₀₀} {f₂₁ : A₂₂ → A₂₀} {f₄₁ : A₄₂ → A₄₀}
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-- {f₀₃ : A₀₂ → A₀₄} {f₂₃ : A₂₂ → A₂₄} {f₄₃ : A₄₂ → A₄₄}
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-- {f₁₀ : A₂₀ → A₀₀} {f₁₂ : A₂₂ → A₀₂} {f₁₄ : A₂₄ → A₀₄}
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-- {f₃₀ : A₂₀ → A₄₀} {f₃₂ : A₂₂ → A₄₂} {f₃₄ : A₂₄ → A₄₄}
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-- (s₁₁ : f₀₁ ∘ f₁₂ ~ f₁₀ ∘ f₂₁) (s₃₁ : f₄₁ ∘ f₃₂ ~ f₃₀ ∘ f₂₁)
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-- (s₁₃ : f₀₃ ∘ f₁₂ ~ f₁₄ ∘ f₂₃) (s₃₃ : f₄₃ ∘ f₃₂ ~ f₃₄ ∘ f₂₃)
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structure three_by_three_span : Type :=
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{A₀₀ A₂₀ A₄₀ A₀₂ A₂₂ A₄₂ A₀₄ A₂₄ A₄₄ : Type}
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{f₁₀ : A₂₀ → A₀₀} {f₃₀ : A₂₀ → A₄₀}
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{f₁₂ : A₂₂ → A₀₂} {f₃₂ : A₂₂ → A₄₂}
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{f₁₄ : A₂₄ → A₀₄} {f₃₄ : A₂₄ → A₄₄}
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{f₀₁ : A₀₂ → A₀₀} {f₀₃ : A₀₂ → A₀₄}
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{f₂₁ : A₂₂ → A₂₀} {f₂₃ : A₂₂ → A₂₄}
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{f₄₁ : A₄₂ → A₄₀} {f₄₃ : A₄₂ → A₄₄}
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(s₁₁ : f₀₁ ∘ f₁₂ ~ f₁₀ ∘ f₂₁) (s₃₁ : f₄₁ ∘ f₃₂ ~ f₃₀ ∘ f₂₁)
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(s₁₃ : f₀₃ ∘ f₁₂ ~ f₁₄ ∘ f₂₃) (s₃₃ : f₄₃ ∘ f₃₂ ~ f₃₄ ∘ f₂₃)
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open three_by_three_span
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variable (E : three_by_three_span)
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-- check (pushout.functor (f₂₁ E) (f₀₁ E) (f₄₁ E) (s₁₁ E) (s₃₁ E))
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definition pushout2hv (E : three_by_three_span) : Type :=
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pushout (pushout.functor (f₂₁ E) (f₀₁ E) (f₄₁ E) (s₁₁ E) (s₃₁ E))
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(pushout.functor (f₂₃ E) (f₀₃ E) (f₄₃ E) (s₁₃ E) (s₃₃ E))
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definition pushout2vh (E : three_by_three_span) : Type :=
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pushout (pushout.functor (f₁₂ E) (f₁₀ E) (f₁₄ E) (s₁₁ E)⁻¹ʰᵗʸ (s₁₃ E)⁻¹ʰᵗʸ)
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(pushout.functor (f₃₂ E) (f₃₀ E) (f₃₄ E) (s₃₁ E)⁻¹ʰᵗʸ (s₃₃ E)⁻¹ʰᵗʸ)
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definition three_by_three (E : three_by_three_span) : pushout2hv E ≃ pushout2vh E := sorry
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end
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end pushout
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