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add psquares with two constant sides

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Floris van Doorn 2018-09-05 17:58:38 +02:00
parent 86c375b0c4
commit 04c80c477f
2 changed files with 16 additions and 11 deletions
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21
hott/types/pointed.hlean
View file

@ -197,7 +197,7 @@ namespace pointed
definition pconst [constructor] (A B : Type*) : A →* B := definition pconst [constructor] (A B : Type*) : A →* B :=
!ppi_const !ppi_const
-- the pointed type of pointed maps -- TODO: remove -- the pointed type of pointed maps
definition ppmap [constructor] (A B : Type*) : Type* := definition ppmap [constructor] (A B : Type*) : Type* :=
@pppi A (λa, B) @pppi A (λa, B)
@ -327,6 +327,12 @@ namespace pointed
definition is_equiv_pcast [instance] {A B : Type*} (p : A = B) : is_equiv (pcast p) := definition is_equiv_pcast [instance] {A B : Type*} (p : A = B) : is_equiv (pcast p) :=
!is_equiv_cast !is_equiv_cast
definition pcompose_pconst [constructor] (f : B →* C) : f ∘* pconst A B ~* pconst A C :=
phomotopy.mk (λa, respect_pt f) (idp_con _)⁻¹
definition pconst_pcompose [constructor] (f : A →* B) : pconst B C ∘* f ~* pconst A C :=
phomotopy.mk (λa, rfl) !ap_constant⁻¹
/- categorical properties of pointed homotopies -/ /- categorical properties of pointed homotopies -/
variable (k) variable (k)
@ -1211,10 +1217,10 @@ namespace pointed
variables {A' A₀₀ A₂₀ A₄₀ A₀₂ A₂₂ A₄₂ A₀₄ A₂₄ A₄₄ : Type*} variables {A' A₀₀ A₂₀ A₄₀ A₀₂ A₂₂ A₄₂ A₀₄ A₂₄ A₄₄ : Type*}
{f₁₀ f₁₀' : A₀₀ →* A₂₀} {f₃₀ : A₂₀ →* A₄₀} {f₁₀ f₁₀' : A₀₀ →* A₂₀} {f₃₀ : A₂₀ →* A₄₀}
{f₀₁ f₀₁' : A₀₀ →* A₀₂} {f₂₁ f₂₁' : A₂₀ →* A₂₂} {f₄₁ : A₄₀ →* A₄₂}
{f₁₂ f₁₂' : A₀₂ →* A₂₂} {f₃₂ : A₂₂ →* A₄₂} {f₁₂ f₁₂' : A₀₂ →* A₂₂} {f₃₂ : A₂₂ →* A₄₂}
{f₀₃ : A₀₂ →* A₀₄} {f₂₃ : A₂₂ →* A₂₄} {f₄₃ : A₄₂ →* A₄₄}
{f₁₄ : A₀₄ →* A₂₄} {f₃₄ : A₂₄ →* A₄₄} {f₁₄ : A₀₄ →* A₂₄} {f₃₄ : A₂₄ →* A₄₄}
{f₀₁ f₀₁' : A₀₀ →* A₀₂} {f₂₁ f₂₁' : A₂₀ →* A₂₂} {f₄₁ : A₄₀ →* A₄₂}
{f₀₃ : A₀₂ →* A₀₄} {f₂₃ : A₂₂ →* A₂₄} {f₄₃ : A₄₂ →* A₄₄}
definition psquare [reducible] (f₁₀ : A₀₀ →* A₂₀) (f₁₂ : A₀₂ →* A₂₂) definition psquare [reducible] (f₁₀ : A₀₀ →* A₂₀) (f₁₂ : A₀₂ →* A₂₂)
(f₀₁ : A₀₀ →* A₀₂) (f₂₁ : A₂₀ →* A₂₂) : Type := (f₀₁ : A₀₀ →* A₀₂) (f₂₁ : A₂₀ →* A₂₂) : Type :=
@ -1231,10 +1237,15 @@ namespace pointed
definition pvdeg_square {f f' : A →* A'} (p : f ~* f') : psquare f f' !pid !pid := definition pvdeg_square {f f' : A →* A'} (p : f ~* f') : psquare f f' !pid !pid :=
!pid_pcompose ⬝* p ⬝* !pcompose_pid⁻¹* !pid_pcompose ⬝* p ⬝* !pcompose_pid⁻¹*
variables (f₀₁ f₁₀)
variables (f₁₀ f₁₂ f₀₁ f₂₁)
definition hpconst_square : psquare !pconst !pconst f₀₁ f₂₁ :=
!pcompose_pconst ⬝* !pconst_pcompose⁻¹*
definition vpconst_square : psquare f₁₀ f₁₂ !pconst !pconst :=
!pconst_pcompose ⬝* !pcompose_pconst⁻¹*
definition phrefl : psquare !pid !pid f₀₁ f₀₁ := phdeg_square phomotopy.rfl definition phrefl : psquare !pid !pid f₀₁ f₀₁ := phdeg_square phomotopy.rfl
definition pvrefl : psquare f₁₀ f₁₀ !pid !pid := pvdeg_square phomotopy.rfl definition pvrefl : psquare f₁₀ f₁₀ !pid !pid := pvdeg_square phomotopy.rfl
variables {f₀₁ f₁₀} variables {f₁₀ f₁₂ f₀₁ f₂₁}
definition phrfl : psquare !pid !pid f₀₁ f₀₁ := phrefl f₀₁ definition phrfl : psquare !pid !pid f₀₁ f₀₁ := phrefl f₀₁
definition pvrfl : psquare f₁₀ f₁₀ !pid !pid := pvrefl f₁₀ definition pvrfl : psquare f₁₀ f₁₀ !pid !pid := pvrefl f₁₀

6
hott/types/pointed2.hlean
View file

@ -454,12 +454,6 @@ namespace pointed
end end
/- properties of ppmap, the pointed type of pointed maps -/ /- properties of ppmap, the pointed type of pointed maps -/
definition pcompose_pconst [constructor] (f : B →* C) : f ∘* pconst A B ~* pconst A C :=
phomotopy.mk (λa, respect_pt f) (idp_con _)⁻¹
definition pconst_pcompose [constructor] (f : A →* B) : pconst B C ∘* f ~* pconst A C :=
phomotopy.mk (λa, rfl) !ap_constant⁻¹
definition ppcompose_left [constructor] (g : B →* C) : ppmap A B →* ppmap A C := definition ppcompose_left [constructor] (g : B →* C) : ppmap A B →* ppmap A C :=
pmap.mk (pcompose g) (eq_of_phomotopy (pcompose_pconst g)) pmap.mk (pcompose g) (eq_of_phomotopy (pcompose_pconst g))