lean2/hott/homotopy/homotopy.md

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).

• cylinder (Mapping cylinders, defined using quotients)
• susp (Suspensions, defined using pushouts)
• red_susp (Reduced suspensions)
• sphere (Higher spheres, defined recursively using suspensions)
• circle (defined as sphere 1)
• torus (defined as a two-quotient)
• interval (defined as the suspension of unit)
• cellcomplex (general cell complexes)
• connectedness
• cofiber
• smash
• homotopy_group (theorems about homotopy groups. The definition and basic facts about homotopy groups is in algebra/homotopy_group).