Huh, diagram chasing attributed to Lambek? Kind of surprising, but plausible. I would have thought Steenrod would have gotten the credit.
Also, kind of melancholic, this paper is for Lambek's 90th birthday, but it has a publication date two years after his death. I was lucky to attend one of Lambek's lectures and take a course he designed. He was a great expositor, and I'll miss him.
I don't think this attribution makes sense without some further qualification. There is diagram chasing ten years earlier in Cartan-Eilenberg's Homological Algebra (1955) -- they prove the five lemma early on -- and Mac Lane mentions the term in his Homology (1963). I wouldn't be surprised if it appears in Eilenberg-Steenrod, or, as you say, Steenrod's earlier work or the Cartan Seminar notes (which I don't have near me right now).
I am a bit lost. How is cryptography about secrecy of the text through some operation, like a function, while at the same time being a system that defines itself?
Cryptography has nothing to do with secrecy at all. It has to do with maintaining the integrity of the communication (or specifically, the message) given highly active and adversarial entities.
Anyone who thinks they can have security through secrecy (i.e. 'cryptography') is a fool, imo.
> It has to do with maintaining the integrity of the communication
This requires secrecy, or else any adversary can do exactly what you did and fake a message.
Note that it doesn't require secrecy of the method, but it does require secrecy of at least some of the input (a key). Therefore whatever method you use should preserve the secrecy of that input to be suitable for cryptography.
It leverages some cool work of Conal Elliott that develops (formulas in) cartesian closed categories into something like an "intermediate representation" for functional language compilation.
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[ 1.0 ms ] story [ 12.0 ms ] threadAlso, kind of melancholic, this paper is for Lambek's 90th birthday, but it has a publication date two years after his death. I was lucky to attend one of Lambek's lectures and take a course he designed. He was a great expositor, and I'll miss him.
Cryptography has nothing to do with secrecy at all. It has to do with maintaining the integrity of the communication (or specifically, the message) given highly active and adversarial entities.
Anyone who thinks they can have security through secrecy (i.e. 'cryptography') is a fool, imo.
This requires secrecy, or else any adversary can do exactly what you did and fake a message.
Note that it doesn't require secrecy of the method, but it does require secrecy of at least some of the input (a key). Therefore whatever method you use should preserve the secrecy of that input to be suitable for cryptography.
http://newartisans.com/2017/04/haskell-and-z3/
It leverages some cool work of Conal Elliott that develops (formulas in) cartesian closed categories into something like an "intermediate representation" for functional language compilation.
http://conal.net/blog/posts/haskell-to-hardware-via-cccs http://conal.net/blog/posts/overloading-lambda
http://conal.net/papers/compiling-to-categories/ (the "LaTeX goals" ICFP 2017 paper)
--
Also, something I always like to link when this kind of thing comes up: the salamander lemma!
https://sbseminar.wordpress.com/2007/11/13/anton-geraschenko...
https://mathoverflow.net/questions/6749/a-proof-of-the-salam...