52dd6cf90b
This commit adds truncated 2-quotients, groupoid quotients, Eilenberg MacLane spaces, chain complexes, the long exact sequence of homotopy groups, the Freudenthal Suspension Theorem, Whitehead's principle, and the computation of homotopy groups of almost all spheres which are known in HoTT.
1.8 KiB
1.8 KiB
homotopy
Development of Homotopy Theory, including basic hits (higher inductive types; see also hit). The following files are in this folder (sorted such that files only import previous files).
- connectedness (n-Connectedness of types and functions)
- cylinder (Mapping cylinders, defined using quotients)
- susp (Suspensions, defined using pushouts)
- sphere (Higher spheres, defined recursively using suspensions)
- circle (defined as sphere 1)
- interval (defined as the suspension of unit)
- cellcomplex (general cell complexes)
- cofiber
- wedge
- smash
- join
- freudenthal (The Freudenthal Suspension Theorem)
- hopf (the Hopf construction and delooping of coherent connected H-spaces)
- complex_hopf (the complex Hopf fibration)
- imaginaroid (imaginaroids as a variant of the Cayley-Dickson construction)
- quaternionic_hopf (the quaternionic Hopf fibration)
- chain_complex
- LES_of_homotopy_groups
- homotopy_group (theorems about homotopy groups. The definition and basic facts about homotopy groups is in algebra/homotopy_group)
- sphere2 (calculation of the homotopy group of spheres)
The following files depend on hit.two_quotient which on turn depends on circle.