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 Feb 18 awarded Nice Question Dec 11 awarded Notable Question Dec 11 awarded Teacher Oct 2 awarded Popular Question Jul 8 awarded Nice Question Feb 26 awarded Notable Question Jan 11 awarded Yearling Jul 2 awarded Curious Dec 18 awarded Popular Question Oct 28 accepted What is $R(\omega)$ (and where can I find definitions for similar common notation)? Oct 28 comment What is $R(\omega)$ (and where can I find definitions for similar common notation)? Ah, thanks. It helps to know that $R(\omega)$ is called the "rank function". Oct 28 asked What is $R(\omega)$ (and where can I find definitions for similar common notation)? Oct 25 accepted What's the motivation behind saturated models? Oct 24 asked What's the motivation behind saturated models? Oct 5 accepted Find a set of sentences $\Sigma$ such that the set of all models of $\Sigma$ is countably infinite. Oct 5 revised Find a set of sentences $\Sigma$ such that the set of all models of $\Sigma$ is countably infinite. added 4 characters in body Oct 5 asked Find a set of sentences $\Sigma$ such that the set of all models of $\Sigma$ is countably infinite. Oct 5 accepted Derive adjoint unit from counit Oct 5 comment Derive adjoint unit from counit Thanks. My issue now is that I have trouble proving that $G_{\epsilon_Y} \circ id_{F(G(Y))}^* = id_{G(Y)}$, not because it's particularly difficult, but because I used this fact to prove the naturality of $id_{F(-)}^*$ so I'm not allowed to invoke naturality in my proof. Instead, I invoked the universal mapping property of the counit to claim that $id_{F(-)}^*$ is $\eta$ (and thus is natural), but I don't think this is quite valid. I understand all the parts of the proof, but I haven't had time to sit down and formalize it yet. Hopefully this answer will be sufficient when I do. Sep 21 asked Derive adjoint unit from counit