From the 1 of 9 linked papers with an AI index.
9 papers
Recognizing CGW categories among pointed stable double Segal spaces
Julia E. Bergner, Brandon T. Shapiro, Inna Zakharevich
The paper proves that any CGW category can be interpreted as a pointed stable double Segal space and gives a classifying diagram construction that identifies the two structures, cl…
Equivariant Trees and Partition Complexes
Julia E. Bergner, Peter Bonventre, Maxine E. Calle +2
We introduce two definitions of -equivariant partitions of a finite -set, both of which yield -equivariant partition complexes. By considering suitable notions of equivari…
A comparison of definitions of equivariant trees
Julia E. Bergner, Maxine E. Calle, David Chan +2
We show that various categories of trees can be modeled by Grothendieck constructions on categories of trees with a fixed set of leaves. We prove this result for the dendroidal cat…
Discreteness and completeness for -models of -categories
Julia E. Bergner
We establish cartesian model structures for variants of -spaces in which we replace some or all of the completeness conditions by discreteness conditions. We prove that they…
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…
Simplicial sets in topology, category theory, and beyond
Julia E. Bergner
The notion of a simplicial set originated in algebraic topology, and has also been utilized extensively in category theory, but until relatively recently was not used outside of th…