Talk:Cayley's Theorem (Category Theory)

It is only sort of implied by Awodey that this could be called "Cayley's Theorem", but the analogy is so strong that I don't see a problem with that (unless someone finds how this theorem is properly named). It is not the Yoneda lemma, which is much more powerful. --Lord_Farin 16:18, 9 August 2012 (UTC)

Might be worth adding some words along those lines - people are going to scratch their heads and say "But Cayley predates cat thry by a century ..." --prime mover 16:23, 9 August 2012 (UTC)

I deem the addition just done sufficient at the least. --Lord_Farin 16:46, 9 August 2012 (UTC)

Questions

How does F being an embedding imply being an isomorphism of categories? In addition, the proof can be stated without proof by contradiction. I had some issues defining the inverse functor, so that could be a good addition. --NightRa (talk) 13:49, 13 July 2016 (UTC)

What is $F$? Did you not see the red link? I'm at a loss... — Lord_Farin (talk) 16:28, 13 July 2016 (UTC)

Excuse me, I meant $H$. We arrived at the fact that $H$ is an embedding, and ended the proof stating that $H$ is an isomorphism between the two categories. That last jump is unclear. --NightRa (talk) 16:51, 13 July 2016 (UTC)

This last step follows from (to not say, is) the definition of embedding. You can compare it to an injection being a bijection to its image. — Lord_Farin (talk) 17:02, 13 July 2016 (UTC)