Nate
Reputation
604
Top tag
Next privilege 1,000 Rep.
Create tags
 Feb26 awarded Notable Question Jan11 awarded Yearling Jul2 awarded Curious Dec18 awarded Popular Question Oct28 accepted What is $R(\omega)$ (and where can I find definitions for similar common notation)? Oct28 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". Oct28 asked What is $R(\omega)$ (and where can I find definitions for similar common notation)? Oct25 accepted What's the motivation behind saturated models? Oct24 asked What's the motivation behind saturated models? Oct5 accepted Find a set of sentences $\Sigma$ such that the set of all models of $\Sigma$ is countably infinite. Oct5 comment Find a set of sentences $\Sigma$ such that the set of all models of $\Sigma$ is countably infinite. Cool. $s_0 \lor \lnot s_0 \in \Sigma$ and $s_{n^+} \rightarrow (\lnot s_n \land \ldots) \in \Sigma$, $\mathbb M$ contains $\emptyset$ and singleton subsets of $\mathbb S$. Thanks for the hint! Oct5 revised Find a set of sentences $\Sigma$ such that the set of all models of $\Sigma$ is countably infinite. added 4 characters in body Oct5 asked Find a set of sentences $\Sigma$ such that the set of all models of $\Sigma$ is countably infinite. Oct5 accepted Derive adjoint unit from counit Oct5 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. Sep21 asked Derive adjoint unit from counit Sep13 accepted Equalizers and Basic limit theorem in Category theory Sep13 comment Equalizers and Basic limit theorem in Category theory Yeah, it seems that $I$, $J$, ... are indeed intended to index the objects $D_I$, $D_J$, ... of $\textbf{D}$. Apologies; this syntax is somewhat new to me. Sep13 revised Equalizers and Basic limit theorem in Category theory added 12 characters in body Sep13 comment Equalizers and Basic limit theorem in Category theory Oh, that was just me being sloppy when summarizing the proof in the book. In the book, $I$ and $J$ are the notation used when referring to elements of $V$ (i.e. only in the indexing of the products), while $D_I$ and $D_J$ are used when referring to objects of $\textbf{D}$ (which are indeed the same, unless I'm missing something). Sorry. I'll go back and edit.