Lectures related to Category of topological spaces

Homotopical Algebra: Theory and Applications

Explores homotopical algebra, covering colimits, limits, adjunctions, and their applications in group theory.

Topology Seminar: Tower Sequences and Homomorphisms

Explores tower sequences, homomorphisms, and their applications in topology, including the computation of homology and the construction of telescopes.

Limits and Colimits: Equalizers and Coequalizers

Covers limits and colimits, focusing on equalizers and coequalizers in category theory.

Compact-open topology

Covers the compact-open topology, defining maps between spaces and discussing continuous maps and preimages in topology.

Review of Simplicial Sets

Covers limits, colimits, standard simplices, mapping spaces, boundaries, horns, and spines.

Schematic Models: Quasi-Categories and ∞-Groupoids

Covers schematic models, emphasizing quasi-categories and ∞-groupoids in modeling categories.

Open Mapping Theorem

Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.