Posted by Martin Orr on Saturday, 16 May 2009 at 19:54
In my last post on the Yoneda lemma for groups, I ignored the naturality part of the lemma. I want to work in detail what this means once - it is a lot of fiddly composing of morphisms and I probably won't do it again (at least in public). If you're not in the mood for following such details, then there is little point in reading this, although you could skip to the last paragraph.
Posted by Martin Orr on Sunday, 10 May 2009 at 16:07
When I wrote my first post on Cayley's theorem, I noticed that Wikipedia claims that the Yoneda lemma is "a vast generalisation of Cayley's theorem". In this post I will try to understand why, and end up concluding that this is probably false.
Posted by Martin Orr on Saturday, 02 May 2009 at 17:12
This post explains how we can consider groups as categories, along with treating the G-sets and G-homomorphisms I considered in my last post on group actions as category-theoretic objects. This is preparation for talking about the Yoneda lemma. Before reading this post, you will need to know the definitions of categories, functors and natural transformations.
Posted by Martin Orr on Monday, 27 April 2009 at 13:23
This continues my earlier post on groups and actions. I want to think some more about Cayley's theorem, and describe how it provides an example of a universal property. (With regard to James's comment on that post, I think universality may be a better way than injectivity of describing my concept of "active group" but I'm not sure how to do that in full).
Posted by Martin Orr on Sunday, 15 March 2009 at 22:28
Another term has just finished. This term I studied:
I have also done some work on an essay (worth the same credit as a lecture course) on Complex Multiplication (which is about a special type of elliptic curves). I gave a seminar on this last Friday but beyond the content of that I don't know much about it yet - I shall have to work on it over the holiday.
Other big news is that I have a place at the Université Paris Sud in Orsay for the second year of a French masters next year (because getting funding to go straight to a PhD in Paris would be a problem), and this week I heard I have got the Rouse Ball Travelling Studentship in Mathematics from Trinity to pay for it.