……Milewski 的《Category Theory for Programmers》视频讲座系列。和所有视频讲座一样，它能很好地激励那些还没入门范畴论的 Haskell 程序员。2. Goldblatt 的《Topoi》。虽然相当有年代感了，但通过在 topoi 上的应用把范畴论讲得很透彻。3. MacLane 的《CatWork》（Categories for the Working Mathematician）。我个人不是特别喜欢这本，但硬啃下来是必经之路。最关键的……
…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…
…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…
……非标准分析，但也并非毫无道理。可以挑选以下内容的一个子集阅读，必要时用 nLab 和 Wikipedia 作为补充：0. Milewski 的《Category Theory for Programmers》[0] 1. Goldblatt 的《Topoi》[1] 2. McLarty 的《The Uses and Abuse of the History of Topos Theory》[2]（这篇不需要先读 [1]，它只是推翻了 [1] 中所作的一些历史假设，而且和 McLarty 的其他文章一样，极其……
…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…
……成熟编程语言（哪怕是 C 语言）的形式化语义仍是开放的研究课题（例如参见 PLDI 2015 关于 Semantics 的论文 [3]）。TLDR：verification 真的很难。[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...
…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...
链接的文章让我想起了 Robert Goldblatt 在《Topoi - The Categorial Analysis of Logic》中的一段话：“如果推断出……基础系统主要是作为实际创造数学的基础而发挥作用，那将多少有些误导。……
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.…
…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)
……Milewski 的《Category Theory for Programmers》视频讲座系列。和所有视频讲座一样，它能很好地激励那些还没入门范畴论的 Haskell 程序员。2. Goldblatt 的《Topoi》。虽然相当有年代感了，但通过在 topoi 上的应用把范畴论讲得很透彻。3. MacLane 的《CatWork》（Categories for the Working Mathematician）。我个人不是特别喜欢这本，但硬啃下来是必经之路。最关键的……
…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…
……是经典的。不过通常来说，subobject classifier（子对象分类器）是一个 Heyting 代数，表达了直觉主义逻辑的语义。Goldblatt 也写过一本非常优秀但偏入门的《Topoi》，涵盖了这个逻辑层面。所以从逻辑的角度来看，Sets 范畴反而是个例外。我所说的 internal logic（内蕴逻辑），是指对于每一个 topos，人们都可以利用它的对象以及它们之间的函数来建立一套理论……
…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…
……非标准分析，但也并非毫无道理。可以挑选以下内容的一个子集阅读，必要时用 nLab 和 Wikipedia 作为补充：0. Milewski 的《Category Theory for Programmers》[0] 1. Goldblatt 的《Topoi》[1] 2. McLarty 的《The Uses and Abuse of the History of Topos Theory》[2]（这篇不需要先读 [1]，它只是推翻了 [1] 中所作的一些历史假设，而且和 McLarty 的其他文章一样，极其……
…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…
……成熟编程语言（哪怕是 C 语言）的形式化语义仍是开放的研究课题（例如参见 PLDI 2015 关于 Semantics 的论文 [3]）。TLDR：verification 真的很难。[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...
…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...
链接的文章让我想起了 Robert Goldblatt 在《Topoi - The Categorial Analysis of Logic》中的一段话：“如果推断出……基础系统主要是作为实际创造数学的基础而发挥作用，那将多少有些误导。……
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.…
……沉迷于冷战谍报）《SICP》JS 版（读起来很过瘾，我平时写很多 JS，学到了很多东西，尽管之前花了不少时间学这门语言本身，而我现在还停留在第一章）Goldblatt 的《Topoi》（啃起来很费劲，但范畴论在召唤我）Rovelli 的《时间的秩序》（他的书是我目前遇到过把量子力学可能的本质解释得最清楚的）Rovelli 的《薄暮》（同上）
…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)