# 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} }

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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