Topoi
by Robert Goldblatt · first published 1979
6mentions
2recommended by
6HN commenters
2009–2022first – last mentioned
33% recommend67% neutral
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…Mileweski's Category Theory for Programmers, the video lecture series. As is always the case with video lectures, this one can help motivate a Haskell programmer uninitiated in category theory. 2. Goldblatt's Topoi. It's fairly dated, but teaches category theory well, via its application to topoi. 3. MacLane's CatWork. I'm not especially fond of this one, but it's necessary to work through it. The most important…
on “Ask HN: Is there a website specialized in mathematics courses?” ↗…is classical. In general though the subobject classifier is a heyting algebra which expresses the semantics of intuitionistic logic. There is also a very good, but introductory, book by Goldblatt on Topoi that covers this logical aspect So in terms of logics the category of Sets is the exception. By internal logic I mean that for every topos one builds up a theory using it's objects and function between…
on “Category Theory Illustrated – Logic” ↗…nonstandard analysis, but not totally without reason. Some subset of the following, with nLab and Wikipedia supplementing as necessary: 0. Milewski's "Category Theory for Programmers"[0] 1. Goldblatt's "Topoi"[1] 2. McLarty's "The Uses and Abuses of the History of Topos Theory"[2] (this does not require [1], it just undoes some historical assumptions made in [1] and, like everything else by McLarty, is extraordinarily…
on “Physics, Topology, Logic and Computation: A Rosetta Stone (2009) [pdf]” ↗…of mature programming languages, even C, is still open research (e.g., see papers on Semantics in PLDI [3] 2015). TLDR: verification is hard. [1] https://en.wikipedia.org/wiki/Nicolas_Bourbaki [2] Topoi, the categorial analysis of logic. Goldblatt, Robert. http://digital.library.cornell.edu/cgi/t/text/text-idx?c=mat... [3] http://conf.researchr.org/track/pldi2015/pldi2015-papers#pro...
on “New Paper: Theory of Programs” ↗Linked article reminded me of a passage in "Topoi - The Categorial Analysis of Logic" by Robert Goldblatt: "It would be somewhat misleading to infer [...] that foundational systems act primarily as a basis out of which mathematics is actually created.…
on “What is so wrong with thinking of real numbers as infinite decimals?” ↗…obsessed with Cold War espionage) SICP, JS edition (great read, I do a lot of JS work and I’ve learned a lot, despite time spent studying the language itself, and I’m still in the first chapter) Topoi, Goldblatt (tough read, but Category Theory calls to me) The Order of Time, Rovelli (his work is the clearest explication I’ve yet encountered of how QM might really be) Helgoland, Rovelli (ibid)
on “Ask HN: Which book are you reading, since when?” ↗