Homotopy Type TheoryCovers homotopy type theory, including equivalences, contractible spaces, pushouts, and applications.
Contracting SubspacesExplores the homotopy extension property for contractable subspaces and their quotient maps.
Universal CoveringExplores the concept of a universal cover of a topological space and the necessary conditions for a space to have one.
Homotopy Lifting PropertyExplores the homotopy lifting property, demonstrating how to lift homotopic maps and solve lifting problems on different spaces.
Hurewicz TheoremExplores the proof of the Hurewicz Theorem and its applications to spheres and homotopy groups.
Cohomology: Cross ProductExplores cohomology and the cross product, demonstrating its application in group actions like conjugation.
Homology TheoremCovers the proof of Theorem A, discussing homology, quotients, and isomorphisms.
