37 lines
1.8 KiB
Markdown
37 lines
1.8 KiB
Markdown
homotopy
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========
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Development of Homotopy Theory, including basic hits (higher inductive
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types; see also [hit](../hit/hit.md)). The following files are in this
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folder (sorted such that files only import previous files).
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* [connectedness](connectedness.hlean) (n-Connectedness of types and functions)
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* [cylinder](cylinder.hlean) (Mapping cylinders, defined using quotients)
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* [susp](susp.hlean) (Suspensions, defined using pushouts)
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* [sphere](sphere.hlean) (Higher spheres, defined recursively using suspensions)
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* [circle](circle.hlean) (defined as sphere 1)
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* [interval](interval.hlean) (defined as the suspension of unit)
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* [cellcomplex](cellcomplex.hlean) (general cell complexes)
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* [cofiber](cofiber.hlean)
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* [wedge](wedge.hlean)
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* [smash](smash.hlean)
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* [join](join.hlean)
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* [freudenthal](freudenthal.hlean) (The Freudenthal Suspension Theorem)
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* [hopf](hopf.hlean) (the Hopf construction and delooping of coherent connected H-spaces)
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* [complex_hopf](complex_hopf.hlean) (the complex Hopf fibration)
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* [imaginaroid](imaginaroid.hlean) (imaginaroids as a variant of the Cayley-Dickson construction)
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* [quaternionic_hopf](quaternionic_hopf.hlean) (the quaternionic Hopf fibration)
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* [chain_complex](chain_complex.hlean)
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* [LES_of_homotopy_groups](LES_of_homotopy_groups.hlean)
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* [vankampen](vankampen.hlean) (the Seifert-van Kampen theorem)
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* [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))
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* [sphere2](sphere2.hlean) (calculation of the homotopy group of spheres)
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The following files depend on
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[hit.two_quotient](../hit/two_quotient.hlean) which on turn depends on
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[circle](circle.hlean).
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* [red_susp](red_susp.hlean) (Reduced suspensions)
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* [torus](torus.hlean) (defined as a two-quotient)
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* [EM](EM.hlean): Eilenberg MacLane spaces
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