npub1knzsux7p6lzwzdedp3m8c3c92z0swzc0xyy5glvse58txj5e9ztqpac73p (npub1knz…c73p)
I just read your blog post about the "free 2-rig" and schur functors, and I can't help but laugh at the timing. At the end of the post you show that (for a 2-rig R) every natural endofunctor R --> R is a (schur) polynomial, and you compare this to the decategorified case of every natural function R --> R (for a ring R, now) is a polynomial.
(Also, I'm sure you know this, but for other readers, in both cases here "natural" is meant in the technical sense of "defined uniformly for all 2-rigs (resp. rings) R")
The timing is funny because npub1ch8hfpny6tp95jqut4smklg3nx2h93dvvw6x4jsaqzwj8u6az9lqfw3ckt (npub1ch8…3ckt) recently posted a blog post of his own working out the decategorified version in detail!
And for anyone who hasn't seen them yet, here are the two posts I'm referencing:
https://golem.ph.utexas.edu/category/2023/10/the_free_2rig_on_one_object.html
https://terrytao.wordpress.com/2023/08/25/yonedas-lemma-as-an-identification-of-form-and-function-the-case-study-of-polynomials/
Chris Grossack /
npub1nm…7zf3z
2023-10-03 06:18:06
Author Public Key
npub1nmn8ycse53ftzklmtv42g4g4dhha35fgjfnx650x0hxcqg3w6n2s87zf3zPublished at
2023-10-03 06:18:06Event JSON
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"content": "nostr:npub1knzsux7p6lzwzdedp3m8c3c92z0swzc0xyy5glvse58txj5e9ztqpac73p \n\nI just read your blog post about the \"free 2-rig\" and schur functors, and I can't help but laugh at the timing. At the end of the post you show that (for a 2-rig R) every natural endofunctor R --\u003e R is a (schur) polynomial, and you compare this to the decategorified case of every natural function R --\u003e R (for a ring R, now) is a polynomial.\n\n(Also, I'm sure you know this, but for other readers, in both cases here \"natural\" is meant in the technical sense of \"defined uniformly for all 2-rigs (resp. rings) R\")\n\nThe timing is funny because nostr:npub1ch8hfpny6tp95jqut4smklg3nx2h93dvvw6x4jsaqzwj8u6az9lqfw3ckt recently posted a blog post of his own working out the decategorified version in detail!\n\nAnd for anyone who hasn't seen them yet, here are the two posts I'm referencing:\n\nhttps://golem.ph.utexas.edu/category/2023/10/the_free_2rig_on_one_object.html\n\nhttps://terrytao.wordpress.com/2023/08/25/yonedas-lemma-as-an-identification-of-form-and-function-the-case-study-of-polynomials/",
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