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Bartosz Milewski's Programming Cafe
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Latest posts
Last updated 9 days ago
Profunctor Equipment
9 days ago
The fundamental premise of category theory is that it’s possible to fully...
The Axiom of Univalence
about 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
7 months ago
Previously: Models of (Dependent) Type Theory. There is a deep connection between...
Models of (Dependent) Type Theory
8 months ago
Previously: (Weak) Factorization Systems. It’s been known since Lambek that typed lambda...
(Weak) Factorization Systems
9 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
11 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...
Understanding Attention in LLMs
about 1 year ago
There are many excellent AI papers and tutorials that explain the attention...
Legalizing Comonad Composition
over 1 year ago
The yearly Advent of Code is always a source of interesting coding...