>> 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...