We proved that all the usual things are equivalent to the axiom of choice: Zorn’s lemma, the well ordering principle, cardinal comparability (given two sets, one must inject into the other), and the ...

every family of well ordered sets has a least member — informally, “the well ordered sets are well ordered”; ...

Nov 7, 2024 00:45 Here’s a way to argue that Gerard’s solution to my puzzle is correct. Thurston showed that any star of the ...

Gerard Westendorp has a real knack for geometry, and here is his answer. Here is Thurston’s procedure. First draw the lattice of Eisenstein integers in the complex plane: ...

Previously: Part 6. Next: Part 8. As the course continues, the axioms fade into the background. They rarely get mentioned these days. Much more often, the facts we’re leaning on are theorems that were ...

Previously: Part 5. Next: Part 7. A category theorist might imagine that a chapter with this title would be about constructing colimits, and they’d be half right.

Are you interested in using category-theoretic methods to tackle problems in topics like quantum computation, machine learning, numerical analysis or graph theory? Then you might like the Adjoint ...

W. P. Thurston, Shapes of polyhedra and triangulations of the sphere. Let me describe one of the key ideas as simply as I can. If you cut out the yellow shape here, you can fold it up along the red ...

You can now apply for the 2025 Summer Research Associate program at the Topos Institute! This is a really good opportunity. Details and instructions on how to apply are in the official announcement. A ...

The Octoberfest is a noble tradition in category theory: a low-key, friendly conference for researchers to share their work and thoughts. This year it’s on Saturday October 26th and Sunday October ...