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The reason I bored you with the Yoneda equipment was to eventually double back to Tannakian reconstruction.
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Working with double categories can be aptly summarized in a meme: Talk to me about sets without mentioning sets.
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You may think of Tannakian Reconstruction as an example of redundant encoding.
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Two friends, Alice and Bob, live in the same city, but on the opposite sides of a wide river.
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I was originally attracted to category theory when trying to understand Haskell optics.
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Previously: Kan Extensions in Double Categories.
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Previously: Kan extensions in Haskell.
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Previously: Tabulation Tribulations.
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Previously: Bending, Yanking, and Cartesian Squares in Double Categories.
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Previously: Profunctor Equipment in Haskell.
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Previously: Profunctor Equipment.
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The fundamental premise of category theory is that it’s possible to fully capture the nature of objects by describing their interactions with other objects of the same type.