3 papers
math.GT2026
Graded-fusion 2-categories and quantum homotopy invariants of 4-manifolds
Matthew Cellot
We introduce 3-group-graded extensions of fusion 2-categories, where 3-groups are modeled by 2-crossed modules. From this data, we derive a state-sum invariant of 4-manifolds equip…
math.QA2025
Higher tensor categories and their extensions: notes from the Scottish Talbot On Algebra and Topology
Diogo Andrade, Julia Bierent, Jennifer Brown +28
These lecture notes are the product of a week-long learning workshop on the work of Johnson-Freyd and Reutter on the problem of the existence of minimal nondegenerate extensions of…
math.AT2025
Higher path groupoids and the holonomy of formal power series connections
Matthew Cellot
Building on ideas of Kohno, we develop a framework for the construction of higher holonomy functors via the transport of formal power series connections. Using these techniques, we…