Syllabus

Proposed Schedule

The following schedule takes us from now through the end of the summer and covers the entirety of the book.  Hopefully everyone will be able to participate through the end, though some may have additional pressures as the beginning of the Fall  sees the start of other courses. Without much prior experience in the field myself, I’ve generally broken things up to cover about 35 pages a week, though some have slightly more or less.  Many, like me, may feel like the text really doesn’t begin until week three or four as the early chapters provide an introduction and cover basic concepts like sets and functions which I have a feeling most have at least some experience with.  I’ve read through chapter two fairly quickly already myself.  This first easy two week stretch will also give everyone the ability to settle in as well as allow others to continue to join the group before we make significant headway.

If anyone has more experience in the subject and wishes to comment on which sections we may all have more conceptual issues with, please let us know so we can adjust the schedule as necessary.  I suppose we may modify the schedule as needed going forward, though like many of you, I’d like to try to cover as much as we can before the end of the summer.

Week One: May 24 (24 pages)

Administrative tasks

  • Purchase Textbook
  • Decide on best day/time for meeting
  • Decide on platform for meetings: Google Hangouts /Skype /ooVoo /Other
  • 1 A brief history of category theory
  • 1.2 Intention of this book
  • 1.3 What is requested from the student
  • 1.4 Category theory references
  • 2 The Category of Sets 9
  • 2.1 Sets and functions
  • 2.2 Commutative diagrams

Meeting:  Friday, June 5, 2015 at 6:45 pm Pacific / 9:45 pm Eastern on Google Hangouts.

Week Two: May 31  (50 pages)

  • 2.3 Ologs
  • 3 Fundamental Considerations in Set 41
  • 3.1 Products and coproducts
  • 3.2 Finite limits in Set

Meeting: Monday, June 8, 2015 at 6:45 pm Pacific / 9:45 pm Eastern on Google Hangouts.

Week Three: June 7 (40 pages)

  • 3.3 Finite colimits in Set
  • 3.4 Other notions in Set

Meeting: Monday, June 15, 2015 at 6:45 pm Pacific / 9:45 pm Eastern on Google Hangouts.

Week Four: June 14 (31 pages)

  • 4 Categories and Functors, Without Admitting It 115
  • 4.1 Monoids

Meeting: Monday, June 22, 2015 at 6:45 pm Pacific / 9:45 pm Eastern on Google Hangouts.

Week Five: June 22 (38 pages)

  • 4.2 Groups

Meeting: Monday, June 29, 2015 at 6:45 pm Pacific / 9:45 pm Eastern on Google Hangouts.

Week Off for Fourth of July Holiday in US

Have some fun and maybe (?) spend some time catching  up if you’re behind…

Week Six: July 6 (16 pages)

  • 4.3 Graphs

Meeting: Monday, July 13, 2015 at 6:45 pm Pacific / 9:45 pm Eastern on Google Hangouts.

Week Seven: July 12 (40 pages)

  • 4.4 Orders
  • 4.5 Databases: schemas and instances [optional coverage]

Meeting: Monday, July 20, 2015 at 6:45 pm Pacific / 9:45 pm Eastern on Google Hangouts.

Week Eight: July 19

  • 5 Basic Category Theory 203

Meeting: Monday, July 27, 2015 at 6:45 pm Pacific / 9:45 pm Eastern on Google Hangouts.

Week Nine: July 26

  • 5.1 Categories and functors

Meeting: Monday, Aug 3, 2015 at 6:45 pm Pacific / 9:45 pm Eastern on Google Hangouts.

Week Ten: August 2

  • 5.1 Categories and functors
  • 5.2 Common categories and functors from pure math

Meeting: Monday, Aug 10, 2015 at 6:45 pm Pacific / 9:45 pm Eastern on Google Hangouts.

Week Eleven: August 9

  • 5.3 Natural transformations (hopefully we’ll start this in our meeting this week)
  • 5.4 Categories and schemas are equivalent, Cat » Sch
  • 6 Fundamental Considerations of Categories
  • 6.1 Limits and colimits
  • 6.2 Other notions in Cat

Meeting: Monday, Aug 17, 2015 at 6:45 pm Pacific / 9:45 pm Eastern on Google Hangouts.

Week Twelve: August 16 (26 pages)

  • 7 Categories at Work 375
  • 7.1 Adjoint functors

Meeting: Monday, Aug 24, 2015 at 6:45 pm Pacific / 9:45 pm Eastern on Google Hangouts.

Week Thirteen: August 23  (32 pages)

  • 7.2 Categories of functors

Meeting: Monday, Aug 31, 2015 at 6:45 pm Pacific / 9:45 pm Eastern on Google Hangouts.

Week Fourteen:  August 30 (19 pages)

  • 7.3 Monads

Week Fifteen:  (23 pages)

  • 7.4 Operads

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Summer Study Group 2015

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