# Week Seven Meeting: §4.4 and §4.5

## Week Seven

This week’s Google Hangout (RSVP here) will cover problems/questions from week seven of the syllabus:

• 4.4 Orders
• 4.5 Databases: schemas and instances

If you’re joining us in progress, please feel free to add in any questions you might have about previous material as well – it’s never too late to join us all.

If you’re stuck and can’t make it, it will be archived (barring any further technical difficulties) on our YouTube Channel for later consumption.

According to the definition:

A graph (V, A, src, tgt) involves two sets and two functions. For two graphs to be comparable, their two sets and their two functions should be appropriately comparable. Let G = (V, A, src, tgt) and G′ = (V′, A′, src′, tgt′) be graphs. A graph homomorphism f from G to G′, denoted f : GG′, consists of two functions f0: VV′ and f1: AA′ …the rest…

So this means that not all elements of A’ need to have a mapping from A and not all elements of V’ need to have a mapping from V. For example if G has m vertices and n edges and G’ has m'(>1) vertices and n'(>1) edges we could have all vertices of G go to one vertex of G'(say a) and all edges of G go to an edge from a to a(assuming that exists) in G’. That would be a valid homomorphism. Am I understanding that correctly ?

# Week Six Meeting: §4.3

## Week Six

This week’s Google Hangout (RSVP here) will cover problems/questions from week six of the syllabus:

• 4.3 Graphs

If you’re joining us in progress, please feel free to add in any questions you might have about previous material as well – it’s never too late to join us all.

If you’re stuck and can’t make it, it will be archived (barring any further technical difficulties) on our YouTube Channel for later consumption.

## Technical Update

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.

## Pace of Material & Syllabus

Some will notice that we’ve slowed down a tad to accommodate the peleton who have been doing the diligence to keep up. Hopefully the last week “off” for the July 4th holiday in the states will have let everyone catch up a bit.  The syllabus will be changing to meet our needs as we proceed.

For those with some general background in Category Theory, we’ll be getting into the serious material shortly.

# Week Five Meeting: §4.2

First apologies that technical difficulties prevented us from recording this week’s session — which incidentally may have been the best yet. Special thanks to those who joined us and helped to make it an interesting conversation.

Based on a few incoming emails as well as the feedback from the group in our conversation last Monday, it’s been suggested that we deviate a bit from our syllabus to slow things down a tad. Hopefully this will help everyone catch up and absorb the material we’re working on.

This week’s Google Hangout (RSVP here) will cover problems/questions from week five of the syllabus:

• 4.2 Groups

If you’re joining us in progress, please feel free to add in any questions you might have about previous material as well – it’s never too late to join us all.

If you’re stuck and can’t make it, it will be archived (barring any further technical difficulties) on our YouTube Channel for later consumption.

## Reminders

Many are keeping regular office hours, or are even generally available to help others out. Please be sure to use them if you need a bit of extra help.

You can also login and make a post here if you’d like. [Example]

In last week’s session, Mark Gomer has also specifically and graciously offered to help anyone who might need it.

I’ll also note that many of us keep the old window from past hangouts open throughout the week, so you can always hop in and see if anyone is available there as well.

# Exercise 4.1.1.7

Could someone explain Exercise 4.1.1.7?

Find an operation on the set $M = \{1, 2, 3, 4\}$, i.e., a legitimate function $f : M \times M \rightarrow M$, such that $f$ cannot be the multiplication formula for a monoid on $M$. That is, either it is not associative or no element of $M$ can serve as a unit.

Sincerely,
Max

# Week Four Meeting: §4.1 – §4.2

This week’s Google Hangout (RSVP here) will cover problems/questions from week four of the syllabus:

• 4.1 Monoids
• 4.2 Groups

If you’re joining us in progress, please feel free to add in any questions you might have about previous material as well – it’s never too late to join us all.

Those who aren’t able to jump into the hangout (due to hardware issues or the 10 person limit) are encouraged to chat within the hangout IM and follow along with the live stream. If you’re stuck and can’t make it, it will be archived on our YouTube Channel for later consumption.

## Participant count

As of this week there are now 32 participants in the group! Thanks to everyone who is participating, as I expected we’d have only about 4 when we started this whole thing.