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Will Jump (Jun 16 2026 at 16:46):In the (Awesome!) graphical linear algebra blog there are some comments talking about doing continued fractions via graphical linear algebra. Did this ever get written down somewhere/ discussed further? Similarly has anyone tried to extend graphical linear algebra to cover infinite dimensions/ functional analysis, is there a synthetic (in the sense of markov categories or graphical linear algebra) study of functional analysis?
Cheers!
John Baez (Jun 17 2026 at 22:44):Probably best to flag the author of that blog, @Pawel Sobocinski.
Pawel Sobocinski (Jun 22 2026 at 09:32):Hi Will -- I half worked out the details long ago but never published it. As far as extensions of GLA, there has been a lot of work in recent years. In particular, this beautiful paper is hot off the press: https://arxiv.org/abs/2605.13993
Cole Comfort (Jul 07 2026 at 06:43):Adding to Pawel, here is a non-exhaustive list of presentations for categories of relations:
Graphical Affine Algebra
Diagrammatic Polyhedral Algebra
Graphical Quadratic Algebra
Graphical Piecewise-Linear Algebra
Graphical Algebraic Geometry
And some stuff by me and my coauthors
Graphical Symplectic Algebra/Stabilizer ZX-calculus
Graphical Quantum Gaussian Algebra/Gaussian ZX-calculus
Delayed ZX-calculus
Maybe it would be useful if I kept track of a list of them.