Are we not doing meetings anymore ? I did not get invites for last week or this week.
- 5.1 Categories and functors
- 5.2 Common categories and functors from pure math
Last week we made it through most of section 5.1, so we’ll finish it up and hopefully make it through 5.2, and pending time and people’s motivation this past week, possibly break into the beginning of 5.3.
We’re behind our original schedule, but still making some relatively good progress with a core peleton of people. Given the participation, we’ve slowed down a tad in an effort to not lose anyone, particularly with a variety of schedules and time zones.
Now that we’re into chapter 5 where the real fun has begun, people might also consider branching out to some of the alternative and more advanced texts. Some of the video resources are probably more germane to everyone now as well. In particular, I spent some time last week with Dr. Codrington’s youtube videos (1-6 of his “Lesson One”) which are generally excellent and which follow reasonably enough the presentation of Spivak that one won’t become lost.
Again, as a reminder for those who have had difficulties joining in the weekly live conversation, be sure to log into Google+ a few minutes before the start of the meeting. Once it starts the moderators send out additional invitation reminders to join the conversation which should result in a pop up on your Google+ page inviting you into the live video/audio feed.
Alternately you can go to the Category Theory Study Group’s Google+ posts page where you should see a button with a camera icon on the particular week’s post that says “Join Hangout”. Clicking it should put you into the live conversation.
Another option should be to join from your events page. If you don’t see the hangout event there, make sure we have your G+ account so we can ensure you’re included in the invitation.
The author is asking about Homomorphism of FLin. In section 4.4.4 he talks about morphism of orders. If s1 <= s2 then f(s1) <= f(s2). Also, order is reflexive (s <= s). So when we have a morphism from FLin to FLin we need to pick 3 elements in FLin so that they are related like they were in FLin. The 3 elements we need to map are 0, 1, 2. If we map 0 in FLin to 3 in FLin then
f(0) = 3
In FLin 0 <= 1. So f(0) <= f(1). If f(0) is 3 then f(1) and f(2) has to be 3 for f(0) <= f(1) and f(0) <= f(2) and f(1) <= f(2). Basically we need to find 3 non decreasing elements in FLin. Rest is combinatorics.