Tannakian Reconstruction

https://bartoszmilewski.com/2026/07/14/tannakian-reconstruction/

by ibobev • 8 days ago

34 3 8 days ago

derbOac• 5 days ago

I admit I didn't follow this as much as I'd like to, and I wish it had some discussion of how this maps onto traditional signal processing frameworks in statistics and information theory, if it does.

JadeNB• 5 days ago

Depending on your mathematical background, it may be easier to get a grasp on Tannaka duality, of which I assume, but don't know, this may usefully be viewed as a (possibly too) vast generalization.

https://en.wikipedia.org/wiki/Tannaka%E2%80%93Krein_duality

YeGoblynQueenne• 5 days ago

> Two friends, Alice and Bob, live in the same city, but on the opposite sides of a wide river. Every night, Bob looks at the lights on the other side and tries to guess, which one belongs to Alice. They come up with a clever arrangement: Alice will turn on her lights for 10 minutes every night at 10 p.m. Every night Bob will take a long-exposure photo at the pre-arranged time. At the end of the year, Bob will superimpose all the photos, and hopefully the only bright spot will be Alice’s window. This is Tannakian reconstruction in a nutshell.

Oh. That's cool. I totally get it. Simple!

> A functor produces a picture of one category inside another. It’s a potentially lossy encoding, but it always preserves the structure of the source. If there is a connection (morphism) between two objects in the source category, there will always be a connection between their images in the target category.

Whaat the fffff...

Tannakian Reconstruction

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