3 papers
math.AT2025
2-Segal sets from cuts of rooted trees
Julia E. Bergner, Olivia Borghi, Pinka Dey +2
The theory of 2-Segal sets has connections to various important constructions such as the Waldhausen -construction in algebraic -theory, Hall algebras, and (co)operad…
math.QA2024
On differential Hopf algebras and algebras
Imma Gálvez-Carrillo, MarÃa Ronco, Andy Tonks
We establish a structure theorem, analogous to the classical result of Milnor and Moore, for differential graded Hopf algebras: any differential Hopf algebra that is free as a…
math.CT2024
Convex decomposition spaces and Crapo complementation formula
Imma Gálvez-Carrillo, Joachim Kock, Andrew Tonks
We establish a Crapo complementation formula for the Möbius function in a general decomposition space in terms of a convex subspace and its complement: $μ^X \simeq…