Decomposition-space slices are toposes

Kock, Joachim; Spivak, David

doi:10.1090/proc/14834

Decomposition-space slices are toposes
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by Joachim Kock and David I. Spivak PDF

Proc. Amer. Math. Soc. 148 (2020), 2317-2329 Request permission

Abstract:

We show that the category of decomposition spaces and CULF maps is locally a topos. Precisely, the slice category over any decomposition space $\mathcal {D}$ is a presheaf topos, namely $\mathsf {Decomp}_{/\mathcal {D}}\simeq \mathsf {Psh}(\operatorname {tw} \mathcal {D})$.

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