Explores fundamental groups, homotopy classes, and coverings in connected manifolds.
Explores the comparison of long exact sequences for vibrations and the relationship between homotopy and homology groups.
Explores solving the homotopic extension problem, constructing relative CW complexes, and ensuring uniqueness in CW approximations.
Explores the construction of cylinder objects in chain complexes over a field, focusing on left homotopy and interval chain complexes.
Explores the CW Approximation Theorem, constructing CW complexes from spaces to ensure isomorphism on homology groups.
Covers fibrant objects, lift of horns, and the adjunction between quasi-categories and Kan complexes, as well as the generalization of categories and Kan complexes.
Explores the uniqueness of CW approximation and Whitehead's theorem through the construction of maps inducing isomorphisms on homotopic groups.
