nLab Birkhoff's theorem


Zoran Škoda writes:

There are several things called “Birkhoff’s theorem” in various field of mathematics and mathematical physics, and belong even to at least 2 different classical Birkhoff’s. Even wikipedia has pages for more than one such theorem. To me the first which comes to mind is Birkhoff’s factorization theorem, now also popular in Kreimer-Connes-Marcolli work and in connection to loop groups (cf. book by Segal and Pressley).

For now we have:


For the theorem as in universal algebra:

William Lawvere considers this Birkhoff’s theorem through the eyes of Isbell duality and cohesive toposes in

  • William Lawvere, Birkhoff’s Theorem from a geometric perspective: A simple example, to appear in Categories and General Algebraic Structures with Applications (2016), journal page.

Last revised on July 12, 2022 at 13:57:32. See the history of this page for a list of all contributions to it.