4 papers
math.RT2025
Tannaka Reconstruction and the Monoid of Matrices
John C. Baez, Todd Trimble
Settling a conjecture from an earlier paper, we prove that the monoid of matrices in a field of characteristic zero is the "walking monoid with a…
math.CT2025
Dirichlet Species and Arithmetic Zeta Functions
John C. Baez
Though Joyal's species are known to categorify generating functions in enumerative combinatorics, they also categorify zeta functions in algebraic geometry. The reason is that any…
math.CT2024
Groupoid Cardinality and Random Permutations
John C. Baez
If we treat the symmetric group as a probability measure space where each element has measure , then the number of cycles in a permutation becomes a random variable. Th…
math.HO2024
The Hexagonal Tiling Honeycomb
John C. Baez
The hexagonal tiling honeycomb is a beautiful structure in 3-dimensional hyperbolic space. It is called {6,3,3} because each hexagon has 6 edges, 3 hexagons meet at each vertex in…