From the 1 of 3 linked papers with an AI index.
3 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…
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…
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…