chore(hott): update default files and some markdown files
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12 changed files with 33 additions and 22 deletions
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@ -4,4 +4,4 @@ Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Floris van Doorn
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Authors: Floris van Doorn
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-/
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-/
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import .functor .set .opposite .product .comma .sum .discrete .indiscrete .terminal .initial
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import .functor .set .opposite .product .comma .sum .discrete .indiscrete .terminal .initial .order
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@ -4,4 +4,4 @@ Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Floris van Doorn
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Authors: Floris van Doorn
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-/
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-/
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import .category .strict .groupoid .constructions
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import .category .strict .groupoid .constructions .limits .functor
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@ -4,4 +4,4 @@ Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Floris van Doorn
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Authors: Floris van Doorn
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-/
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-/
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import .basic
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import .exponential_laws
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@ -4,4 +4,4 @@ Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Floris van Doorn
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Authors: Floris van Doorn
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-/
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-/
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import .limits .colimits
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import .set .functor .adjoint .functor_preserve
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@ -6,7 +6,4 @@ Authors: Floris van Doorn
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The core of the HoTT library
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The core of the HoTT library
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-/
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-/
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import types
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import types cubical homotopy hit choice
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import cubical
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import homotopy.circle
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import algebra.hott
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8
hott/hit/default.hlean
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8
hott/hit/default.hlean
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@ -0,0 +1,8 @@
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/-
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Copyright (c) 2016 Floris van Doorn. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Floris van Doorn
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-/
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import .two_quotient .colimit .coeq .refl_quotient
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@ -10,14 +10,6 @@ open eq is_trunc is_equiv nat equiv trunc prod pushout sigma sphere_index unit
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-- where should this be?
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-- where should this be?
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definition family : Type := ΣX, X → Type
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definition family : Type := ΣX, X → Type
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-- this should be in init!
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namespace nat
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definition cases {M : ℕ → Type} (mz : M zero) (ms : Πn, M (succ n)) : Πn, M n :=
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nat.rec mz (λn dummy, ms n)
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end nat
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namespace cellcomplex
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namespace cellcomplex
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/-
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/-
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8
hott/homotopy/default.hlean
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8
hott/homotopy/default.hlean
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@ -0,0 +1,8 @@
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/-
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Copyright (c) 2016 Floris van Doorn. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Floris van Doorn
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-/
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import .sphere2 .EM .torus .red_susp .quaternionic_hopf .smash .cellcomplex .interval .cylinder
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@ -3,11 +3,12 @@ The Lean Homotopy Type Theory Library
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The Lean Homotopy Type Theory library consists of the following directories:
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The Lean Homotopy Type Theory library consists of the following directories:
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* [init](init/init.md) : constants and theorems needed for low-level system operations
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* [init](init/init.md) : basic definitions and theorems. These are imported in each ".hlean" file by default, unless the `prelude` command is used.
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* [types](types/types.md) : concrete datatypes and type constructors
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* [types](types/types.md) : concrete datatypes and type constructors
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* [hit](hit/hit.md): higher inductive types
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* [algebra](algebra/algebra.md) : algebraic structures, group theory and category theory.
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* [algebra](algebra/algebra.md) : algebraic structures
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* [cubical](cubical/cubical.md) : cubical types (e.g. squares in a types, squareovers)
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* [cubical](cubical/cubical.md): cubical types
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* [hit](hit/hit.md): higher inductive types. Some higher inductive types which are mostly relevant in homotopy theory are in the [homotopy](homotopy/homotopy.md) folder.
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* [homotopy](homotopy/homotopy.md) : synthetic homotopy theory.
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The following files don't fit in any of the subfolders:
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The following files don't fit in any of the subfolders:
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* [prop_trunc](prop_trunc.hlean): in this file we prove that `is_trunc n A` is a mere proposition. We separate this from [types.trunc](types/trunc.hlean) to avoid circularity in imports.
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* [prop_trunc](prop_trunc.hlean): in this file we prove that `is_trunc n A` is a mere proposition. We separate this from [types.trunc](types/trunc.hlean) to avoid circularity in imports.
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@ -16,6 +16,10 @@ namespace nat
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{C : ℕ → Type} (n : ℕ) (H₁ : C 0) (H₂ : Π (a : ℕ), C a → C (succ a)) : C n :=
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{C : ℕ → Type} (n : ℕ) (H₁ : C 0) (H₂ : Π (a : ℕ), C a → C (succ a)) : C n :=
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nat.rec H₁ H₂ n
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nat.rec H₁ H₂ n
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protected definition cases [reducible] [unfold 4] {M : ℕ → Type} (mz : M zero)
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(ms : Πn, M (succ n)) : Πn, M n :=
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nat.rec mz (λn dummy, ms n)
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protected definition cases_on [reducible] [recursor] [unfold 2]
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protected definition cases_on [reducible] [recursor] [unfold 2]
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{C : ℕ → Type} (n : ℕ) (H₁ : C 0) (H₂ : Π (a : ℕ), C (succ a)) : C n :=
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{C : ℕ → Type} (n : ℕ) (H₁ : C 0) (H₂ : Π (a : ℕ), C (succ a)) : C n :=
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nat.rec H₁ (λ a ih, H₂ a) n
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nat.rec H₁ (λ a ih, H₂ a) n
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@ -6,4 +6,4 @@ Authors: Floris van Doorn
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import .bool .unit .prod .sigma .pi .arrow .pointed .fiber
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import .bool .unit .prod .sigma .pi .arrow .pointed .fiber
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import .nat .int
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import .nat .int
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import .eq .equiv .trunc
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import .eq .equiv .trunc .univ .W .type_functor
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@ -30,3 +30,4 @@ Types in HoTT:
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* [trunc](trunc.hlean): truncation levels, n-types, truncation
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* [trunc](trunc.hlean): truncation levels, n-types, truncation
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* [pullback](pullback.hlean)
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* [pullback](pullback.hlean)
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* [univ](univ.hlean)
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* [univ](univ.hlean)
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* [type_functor](type_functor.hlean)
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