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Bartosz Milewski's Programming Cafe

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Latest posts

Last updated 5 days ago

(Weak) Factorization Systems

5 days ago

Previously (Weak) Homotopy Equivalences. An average function between sets, is neither surjective...

(Weak) Homotopy Equivalences

about 1 month ago

Previously: Fibrations and Cofibrations. In topology, we say that two shapes are...

Fibrations and Cofibrations

2 months ago

We are used to thinking of a mapping as either being invertible...

Subfunctor Classifier

3 months ago

Previously: Subobject Classifier. In category theory, objects are devoid of internal structure...

Subobject Classifier

4 months ago

Proviously Sieves and Sheaves. We have seen how topology can be defined...

Understanding Attention in LLMs

5 months ago

There are many excellent AI papers and tutorials that explain the attention...

Legalizing Comonad Composition

7 months ago

The yearly Advent of Code is always a source of interesting coding...

Sieves and Sheaves

9 months ago

Previously: Covering Sieves. We’ve seen an intuitive description of presheaves as virtual...

Covering Sieves

9 months ago

Previously: Sheaves as Virtual Objects. In order to define a sheaf, we...

Sheaves as Virtual Objects

9 months ago

Previously: Coverages and Sites The definition of a sheaf is rather complex...

Coverages and Sites

10 months ago

Previously: Sheaves and Topology. In our quest to rewrite topology using the...

Sheaves and Topology

12 months ago

Previously: Presheaves and Topology. In all branches of science we sooner or...