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Overview
I have been educated in Poland, where I got my PhD in Theoretical Physics. I had several postdoc positions in Europe and in the United States. Then I suddenly found myself working for Microsoft designing and implementing a search engine.
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Profunctor Optics
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: compositi
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Tannakian reconstruction
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
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Tambara Equipment
I was originally attracted to category theory when trying to understand Haskell optics. I was puzzled by the van Laarhoven's functor representations and Kmett's use of Tambara modules. By playing Tetris with the Yoneda lemma I was able to make some progre
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Kan Extensions in Double Categories
Previously: Kan extensions in Haskell. In a double category that is also a proarrow equipment, we have the ability to bend arrows. In particular, in the definition of the counit of the right Kan extension: we can bend the vertical arrow, replacing it with
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Kan Extensions in Haskell
Previously: Tabulation Tribulations. If you think of functor composition as a form of multiplication, Kan extensions are an attempt to construct inverses of this multiplication. But unlike multiplication, composition is not symmetric, so we have extension
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