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• ↓ Profunctor Optics
• ↓ Optics
• ↓ Optics and Tambara modules
• ↓ Haskell implementation
• ↓ Examples
• ↓ Tannakian reconstruction
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"You may think of Tannakian Reconstruction as an example of redundant encoding. It lets you replace a simple hom-set with a much more complex end that is taken over an entire functor category."

"Why would anyone want to do it? The answer is simple: composition! Morphisms on the left compose according to the rules of the category , which can be arbitrarily complex. By contrast, the right hand side lives in , and its elements are functions with very simple composition rules. So any time you want to internalize a non-trivial category in a programming language like Haskell, the Tannakian representation becomes a valuable tool. One such example is the category of optics."

"A simple category of optics over a single category has objects that are pairs of objects . The morphisms are defined using the action of a monoidal category (thus making an actegory):"

"In what follows, we’ll be using the fact that an element of a coend can be constructed by injecting a triple of an object and a pair of morphisms:"

Key Topics & Focus Areas for bartoszmilewski.com:

Profunctor Optics

Optics

Optics and Tambara modules

Haskell implementation

Examples

Tannakian reconstruction