Explains Tannakian reconstruction using an analogy of photos to recover category structure via fiber functors.
Explores Tambara modules in category theory, their relation to Haskell optics, and monoidal functors with code examples.
Explores actegories in programming, starting from monoidal categories and their role in optics like lenses and prisms.
Explores Kan extensions in double categories, generalizing profunctor-based right and left Kan extensions with categorical and Haskell implementations.
Explores tabulation in double categories as an analog of profunctor graphs, using universal properties and 2-cells.
A Haskell tutorial implementing profunctor equipment with functors, profunctors, and 2-cells for category theory enthusiasts.
Explores profunctors in category theory, defining them as heteromorphisms between categories and their role in a double category combining functors and profunctors.
Explores why category theory requires collections larger than sets to be interesting, discussing foundational issues and cardinality.
Explores categorical models for dependent type theory, connecting lambda calculus to fibrations and sections in locally cartesian closed categories.
Explores the concept of (weak) factorization systems in category theory, generalizing function decomposition into surjections and injections.
Explores the categorical definition of a subobject classifier, a key concept in topos theory, using set theory as a foundation.
