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category-theory-2017

This is the webpage for the category theory reading course at ANU for 2017. You might also enjoy watching the Catster's videos. Wikipedia often has quite good content on category theory. A classic book (the early parts of which are quite readable) is MacLane's ''Categories for the working mathematician''.

The plan

Please start reading Tom Leinster's Basic Category Theory.

  • Week 1:
    • An Ran, on the definitions of categories, functors and natural transformations.
    • I encourage you to all bring an example of a natural transformation, and to discuss these examples after An Ran's presentation.
    • I wrote some notes on the problem we discussed, whether all monoids are equivalent to their opposites.
  • Week 2:
    • By the meetings, please finish reading Chapter 1.
    • Zac, on free, faithful, and essentially surjective functors, as well as initial and terminal objects.
  • Week 3:
  • Week 4:
  • Week 5:
  • Week 6:
  • Week 7:
    • Xiang Li spoke more about the Yoneda embedding.
  • Week 8:
    • Scott gave an impromptu talk on David Spivak's interpretation of databases in category theory, and functorial data migration. See his slides for an introduction, or read the paper. This would be a fun topic for a final report!
  • Week 9:
    • James and An Ran will cover the parts of Chapter 5 that we haven't already seen in the assignments.
  • Week 10:
    • Zac and Kie Seng will cover 6.1 and (part of?) 6.2 respectively.

Reports

After your presentation, please write a report (at least one page). It should:

  • State who was there.
  • Indicate the material you covered in your presentation.
  • Note any difficulties or confusions that arose, particularly those that were not resolved in discussion with the group.
  • Indicate the topics covered in the discussion after the presentation.
  • Evaluate your presentation of the material. Could you have arranged things differently, to better aid understanding? Was there too much or too little technical detail? Did you facilitate a constructive discussion after the presentation? Any other comments?

Grading

  • a report on your class presentation (10%)
  • four written assignments (10% each, for 40% total)
  • a final essay (approx. 10 pages, on a topic of your choice related to the material we cover) (35%)
  • a final presentation (by default, on the same topic as your final essay) (15%)

Assignments

The assignment problems will be posted here. The first batch of problems is due at the end of week 4, the second batch is due at the end of week 7. Problems after that are still a work in progress.

Meeting Times

  • Wednesday 12-1: Presentation and discussion
  • Thursday 11-12: Assignment questions discussion
  • Thursday 1-2: Q&A/Lecture with Scott