Locally (co)Cartesian fibrations as realisation fibrations and the classifying space of cospans

Abstract

We show that the conditions in Steimle's 'additivity theorem for cobordism categories' can be weakened to only require \emph{locally} (co)Cartesian fibrations, making it applicable to a larger class of functors. As an application we compute the difference in classifying spaces between the infinity category of cospans of finite sets and its homotopy category.

24 pages, v2: fixed several problems thanks to referee report, to appear in JLMS

References in corpus (3)

• Semi-simplicial spaces
• An Additivity theorem for cobordism categories
• A cobordism model for Waldhausen $K$-theory

Cited by in corpus (5)

• An Additivity theorem for cobordism categories
• The equifibered approach to $\infty$-properads
• The classifying space of the one-dimensional bordism category and a cobordism model for TC of spaces
• Semi-infinite flags and Zastava spaces
• Culf maps and edgewise subdivision