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 …
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
…