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There’s an adjunction between commutative monoids and pointed sets, which gives a comonad. Then:

Take the booleans, apply this comonad and get the natural numbers.

Take the natural numbers, apply this comonad and get Young diagrams.

Take the Young diagrams, apply this comonad and get Schur functors.

Let me explain how this works!

I’ve been talking with Tom Leinster about this lately, so I decided to say more about how it works. You can read it on the n-Category Café:

https://golem.ph.utexas.edu/category/2022/10/partition_function_as_cardinal.html

@xameer yes, I agree it is incredibly fragile and extremely difficult to debug if your formulae does not work as expected. How does one test, observe, or verify each function call in each cell? Your review process grows exponentially depending on the size of the data you are working with.
Why are designers obsessed with hiding stuff on web pages? Scrolling works! Just let me scroll the goddamn page. Don’t send me off on a treasure hunt to click buttons and crap just to see what you’re trying to sell.

The web dev industry’s strategy of trying to discover best practices through broad population surveys (e.g. “State of…”) is just so utterly off-base.

What do you think the result would be like if you surveyed all carpenters, hobbyists, students, masters etc., to discover best practices in carpentry?

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I absolutely don't understand the notifications on mastodon
What kind of algebraic structure is a groupie