Martin's Blog

Naturality in the Yoneda lemma for groups

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.

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Cayley's Theorem and the Yoneda Lemma

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.

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Groups as categories

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.

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