algebraic topology

Recognizing CGW categories among pointed stable double Segal spaces

arXiv:2607.12327

summary

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, clarifying their relationship for algebraic K‑theory.

Abstract

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-theory. In particular, we show that any CGW category can be regarded as a pointed stable double Segal space, and they can be identified using a classifying diagram construction for double categories with shared isomorphisms.

42 pages

Topics & keywords

#cgw categories#double segal spaces#pointed stable structures#classifying diagram#algebraic k-theoryCGW categorypointed stable double Segal spaceclassifying diagram constructiondouble categories with shared isomorphisms
Recognizing CGW categories among pointed stable double Segal spaces · wovepaper