Thomason's colimit theorem for the double category of elements

Andrew Gill; Maru Sarazola

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arXiv · 2506.08246

Thomason's colimit theorem for the double category of elements

Andrew Gill·Maru Sarazola

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Abstract

We show that, for any 2-category $C$ and 2-functor $F\colon C \to Cat$, the double category of elements $\iint_C F$ introduced by Grandis and Par\'e satisfies a version of Thomason's colimit theorem; that is, there is a weak homotopy equivalence $B hocolim F\simeq B(\iint_C F)$.

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Andrew Gill, Maru Sarazola. 2025-06-09. Thomason's colimit theorem for the double category of elements. https://arxiv.org/abs/2506.08246

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