Tambara Equipment
2 days ago
- #Tambara Modules
- #Haskell Programming
- #Category Theory
- Category theory insights were gained from studying Haskell optics, specifically van Laarhoven functor representations and Tambara modules, using the Yoneda lemma.
- Optics are positioned at the intersection of monoidal actions and Tambara modules, with a duality related to Tannakian reconstruction in mathematics.
- Tambara modules can be viewed as horizontal arrows in a double category, which also functions as a proarrow equipment, extending to enriched categories.
- In Haskell, monoidal functors and Tambara modules are implemented through typeclasses, with composition defined for both, forming a bicategory structure.
- Free Tambara modules, constructed via coends, lead to the definition of optics, which can be simplified using internal hom adjunctions and monoidal structures.