Bartosz Milewski
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 progress, attacking more and more esoteric...
Bartosz Milewski
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 its horizontal conjoint . In a profunctor...
Bartosz Milewski
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. Those interactions are encoded using morphisms: arrows between objects. What about categories themselves? We define a...