for all infinite sets X X and Y Y. Proving this required most of the concepts and results from the second half of the course: well ordered sets, the Cantor–Bernstein theorem, the Hartogs theorem, Zorn ...

Earlier this month the Mathematics Institute at Uppsala University hosted a conference called Categorification in Algebra and Topology, clearly a theme close to our collective heart. As yet there are ...

Aug 2, 2008 In this new version of our paper, we systematically explain how n-dimensional field theories give n-plectic manifolds. We also say how a B field affects the 2-plectic structure for a ...

Previously: Part 8. Next: Part 10. It’s the penultimate week of the course, and up until now we’ve abstained from using the axiom of choice. But this week we gorged on it. The section I most enjoyed ...

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

Thurston gave a concrete procedure to construct triangulations of the 2-sphere where 5 or 6 triangles meet at each vertex. How can you get the icosahedron using this procedure? Gerard Westendorp has a ...

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 ...

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 ...

Hello [email protected]. So nice of you to stop by. I'm a member of the Theory Group here at UT. I've been at UT since September 1994. Before coming here, I was an Assistant Professor in the ...