3 papers
math.AT2026
Recognizing CGW categories among pointed stable double Segal spaces
Julia E. Bergner, Brandon T. Shapiro, Inna Zakharevich
In this paper, we establish a precise relationship between CGW categories and pointed stable double Segal spaces, both of which were developed as general input for algebraic K-theo…
math.CT2025
Categorical Tiling Theory: Constructing Directed Planar Tilings via Edge Reversal
Catherine DiLeo, Preston Sessoms, Brandon T. Shapiro
Tilings of the plane resemble the simplicial and other complexes from algebraic topology, but have not been studied from this perspective. We construct finite categories correspond…
math.KT2024
A combinatorial construction of homology via ACGW categories
Maru Sarazola, Brandon Shapiro, Inna Zakharevich
2-Segal spaces arise not only from $S_\dotp$-constructions associated to Waldhausen and (proto) exact categories, but also from $S_\dotp$-constructions associated to certain double…