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Jared Davis

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  • Speaking for the less-experienced, I found Elliott's 2017 talk on the same paper ( http://podcasts.ox.ac.uk/compiling-categories ) a very helpful start.
  • I feel you, Jesus. I have a mysql DB importer that I've got on the docket, and I'm not particularly enthusiastic about the task. I am looking forward to the databases and data-flows portions of the book. I understand these to be Spivak's specialty?
  • Conal Elliott: Could you briefly explain the universal property in section 2 of Compiling to Categories? I don't understand the syntax of the formula given, notably the "double vee": vh. h v f v g v v exl v h v f v exr v h v g
  • Let \( Mat \) be the set of materials, \( \rightarrow \) a reaction, and \( + \) a mixture or combination of materials. Let \( 0 \) signify nothing, e.g. no material. Then we have \( (Mat, \rightarrow, 0, +) \) and (a) \( 2{H}{2}O \rightarrow 2{H}{…
  • I've found an affordable copy of Categories for the Working Philosopher on Amazon. Thank you again for the suggestion; I should be in a better place to get more from the volume after following along with this course the past couple weeks.
  • How should I describe [Anki decks]? Jared Summers gives a good description above: Anki is a smart flash card system. It uses spaced repetition to try to optimize time spent reviewing and learning/memorizing content. I will refrain from po…
  • What is the license on the arXiv document? I'd like to extend Thrina's work with a script; I'd like to ensure I properly respect the authors' rights. I've also noticed that the arXiv docs aren't necessarily the most up-to-date version of the book. I…
  • Start with the empty set. If \( \emptyset \in U \), then so are each of the discreet elements of \( X \). If each of the discreet elements are in the upper set, so are each of the unique pairs, and so on. Finally, the "largest" upper set must be \( …
  • Reflexivity holds For any \( a, b, c \in \tt{R} \) \( a \le b \) and \( b \le c \) implies \( a \le c \) For any \( a, b \in \tt{R} \), \( a \le b \) and \( b \le a \) implies \( a = b \) For any \( a, b \in \tt{R} \), we have either \( a \le b \) …
  • With this exercise, I'd shrink the phrase "the least element that is greater than both A and B" to simply "least greatest". In the context of \( \tt{b} \) I would paraphrase again as "first occurrence of true". So we'd just say the expression short …
  • woof, that's quite a price tag, must be why I haven't gotten my hands on it yet. Looking at the TOC, the essays seem very interesting. Thanks!
  • I'd say \( p \le p \) is true, meaning it must be a meet of A. (too trivial?) Example 1.62 makes it clear that \( p \lor p = p \land p = p \)
  • Is the only difference between a partition and a topology that the empty set is not part of the partition and that the member sets of the partition are disjoint?
  • Ah, I misunderstood the terminology. It's even more obvious: "The most important sort of relationship between preorders is called a monotone map. These are functions that preserve preorder relations[...]" says right on the page :)
  • I'm a bit confused by Remark 1.24. Are Fong & Spivak just saying that what's normally called a "partially ordered set" will be referred to as a "skeletal poset"? It's a bit confusing that a partially ordered set is an extension of something that…
  • I'm uncertain about the first answer I came up with: \( X = { a b c } \) \( Y = { ● ▲ ☐ } \) \( f(a) = ▲ \) \( f(b) = ▲ \text{or} ☐ \) \( f(c) = ● \) then \( P := { { ▲ ☐ } { ● } } \) \( f*({▲ ◻︎}) = { a b } \) \( f*({ ● }) = { c } \) and …
  • Thanks @Scott, your post is immensely clarifying and exactly the sort of thing I hoped for in studying "applied" category theory.