lean2/hott/homotopy/homotopy.md

homotopy
========

Development of Homotopy Theory, including basic hits (higher inductive
types; see also [hit](../hit/hit.md)). The following files are in this
folder (sorted such that files only import previous files).

* [connectedness](connectedness.hlean) (n-Connectedness of types and functions)
* [cylinder](cylinder.hlean) (Mapping cylinders, defined using quotients)
* [susp](susp.hlean) (Suspensions, defined using pushouts)
* [sphere](sphere.hlean) (Higher spheres, defined recursively using suspensions)
* [circle](circle.hlean) (defined as sphere 1)
* [interval](interval.hlean) (defined as the suspension of unit)
* [cellcomplex](cellcomplex.hlean) (general cell complexes)
* [cofiber](cofiber.hlean)
* [wedge](wedge.hlean)
* [smash](smash.hlean)
* [homotopy_group](homotopy_group.hlean) (theorems about homotopy groups. The definition and basic facts about homotopy groups is in [algebra/homotopy_group](../algebra/homotopy_group.hlean)).
* [join](join.hlean)
* [hopf](hopf.hlean) (the Hopf construction and delooping of coherent connected H-spaces)
* [complex_hopf](complex_hopf.hlean) (the complex Hopf fibration)
* [imaginaroid](imaginaroid.hlean) (imaginaroids as a variant of the Cayley-Dickson construction)
* [quaternionic_hopf](quaternionic_hopf.hlean) (the quaternionic Hopf fibration)

The following files depend on
[hit.two_quotient](../hit/two_quotient.hlean) which on turn depends on
[circle](circle.hlean).

* [red_susp](red_susp.hlean) (Reduced suspensions)
* [torus](torus.hlean) (defined as a two-quotient)
refactor(hott): move homotopy hits to new homotopy folder 2015-09-13 18:58:11 +00:00			`homotopy`
			`========`

			`Development of Homotopy Theory, including basic hits (higher inductive`
			`types; see also [hit](../hit/hit.md)). The following files are in this`
			`folder (sorted such that files only import previous files).`

feat(hott): update book.md and homotopy.md to reflect additions 2016-03-07 01:03:27 +00:00			`* [connectedness](connectedness.hlean) (n-Connectedness of types and functions)`
refactor(hott): move homotopy hits to new homotopy folder 2015-09-13 18:58:11 +00:00			`* [cylinder](cylinder.hlean) (Mapping cylinders, defined using quotients)`
			`* [susp](susp.hlean) (Suspensions, defined using pushouts)`
			`* [sphere](sphere.hlean) (Higher spheres, defined recursively using suspensions)`
			`* [circle](circle.hlean) (defined as sphere 1)`
			`* [interval](interval.hlean) (defined as the suspension of unit)`
			`* [cellcomplex](cellcomplex.hlean) (general cell complexes)`
fix(hott): add missing links to markdown files 2016-02-23 18:00:16 +00:00			`* [cofiber](cofiber.hlean)`
feat(hott): update book.md and homotopy.md to reflect additions 2016-03-07 01:03:27 +00:00			`* [wedge](wedge.hlean)`
fix(hott): add missing links to markdown files 2016-02-23 18:00:16 +00:00			`* [smash](smash.hlean)`
feat(hott): update book.md and homotopy.md to reflect additions 2016-03-07 01:03:27 +00:00			`* [homotopy_group](homotopy_group.hlean) (theorems about homotopy groups. The definition and basic facts about homotopy groups is in [algebra/homotopy_group](../algebra/homotopy_group.hlean)).`
			`* [join](join.hlean)`
			`* [hopf](hopf.hlean) (the Hopf construction and delooping of coherent connected H-spaces)`
			`* [complex_hopf](complex_hopf.hlean) (the complex Hopf fibration)`
			`* [imaginaroid](imaginaroid.hlean) (imaginaroids as a variant of the Cayley-Dickson construction)`
			`* [quaternionic_hopf](quaternionic_hopf.hlean) (the quaternionic Hopf fibration)`

			`The following files depend on`
			`[hit.two_quotient](../hit/two_quotient.hlean) which on turn depends on`
			`[circle](circle.hlean).`

			`* [red_susp](red_susp.hlean) (Reduced suspensions)`
			`* [torus](torus.hlean) (defined as a two-quotient)`