幾何学特論II

• Lecture 1: The space of a category.
• Lecture 2: Limits and colimits. Filtered colimits and finite limits of sets commute.
• Lecture 3: Adjoint functors.
• Lecture 4: Characterizing the geometric realization by maps from it.
• Lecture 5: The skeleton filtration of a simplicial set.
• Lecture 6: The geometric realization of a simplicial set is a CW-complex. The category of k-spaces.
• Lecture 7: Geometric realization preserves finite products. Pointed k-spaces.
• Lecture 8: Higher homotopy groups.
• Lecture 9: The mapping fiber and the long exact sequence of homotopy groups.
• Lecture 10: Weak equivalences, Serre fibrations, Serre cofibrations.
• Lecture 11: Quillen model categories.
• Lecture 12: The homotopy category; Quillen functors and their derived functors.
• Lecture 13: The Reedy model structure. Quillen’s Theorem A and Theorem B.