Topology: A Categorical Approach

Book CoverJapanese Edition Cover
Topology: A Categorical Approach is a graduate-level textbook that presents basic topology from the perspective of category theory.

Chapter pdfs are available for free: open access version.

Cover art by London Tsai.


Here are some short videos that supplement the material in the book.

  1. What is topology?
  2. The subspace topology
  3. Paths
  4. Compact and Hausdorff
  5. Filters and Ultrafilters (Part I: no topology)
  6. Filters and Ultrafilters (Part II: convergence and topological properties)
  7. Categorical limits and colimits are unique
  8. Compactifications
  9. Exponential Topologies
  10. The Seifert Van Kampen Theorem
  11. Covering Spaces (Part I: intro and based covers)
  12. The category of G-Sets
  13. Covering Spaces (Part II: the big picture)

These videos are available on the channel YouTube@topology_categorical.