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Bartosz Milewski's Programming Cafe
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Latest posts
Last updated 2 days ago
Bending, Yanking, and Cartesian Squares in Double Categories
2 days ago
Previously: Profunctor Equipment in Haskell. The major advantage of string diagrams is...
Profunctor Equipment in Haskell
5 days ago
Previously: Profunctor Equipment. To make things more palatable for programmers, I decided...
Profunctor Equipment
27 days ago
The fundamental premise of category theory is that it’s possible to fully...
The Axiom of Univalence
2 months ago
Previously: Modeling Identity Types. On first viewing, the identity type seems odd...
Modeling Identity Types
7 months ago
Previously: Identity Types. Let me first explain why the naive categorical model...
Identity Types
8 months ago
Previously: Models of (Dependent) Type Theory. There is a deep connection between...
Models of (Dependent) Type Theory
9 months ago
Previously: (Weak) Factorization Systems. It’s been known since Lambek that typed lambda...
(Weak) Factorization Systems
10 months ago
Previously (Weak) Homotopy Equivalences. An average function between sets, is neither surjective...
(Weak) Homotopy Equivalences
11 months ago
Previously: Fibrations and Cofibrations. In topology, we say that two shapes are...
Fibrations and Cofibrations
12 months ago
We are used to thinking of a mapping as either being invertible...
Subfunctor Classifier
about 1 year ago
Previously: Subobject Classifier. In category theory, objects are devoid of internal structure...
Subobject Classifier
about 1 year ago
Proviously Sieves and Sheaves. We have seen how topology can be defined...