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

@article{Steinebrunner2019LocallyF,
title={Locally (co)Cartesian fibrations as realisation fibrations and the classifying space of cospans},
author={Jan Steinebrunner},
journal={Journal of the London Mathematical Society},
year={2019},
volume={106}
}
• J. Steinebrunner
• Published 16 September 2019
• Mathematics
• Journal of the London Mathematical Society
We show that the conditions in Steimle's ‘additivity theorem for cobordism categories’ can be weakened to only require 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.
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J. Ebert was partially supported by the SFB 878. O. Randal-Williams was supported by EPSRC grant number EP/M027783/1.
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