Thomason's colimit theorem for the double category of elements

Andrew Gill; Maru Sarazola

Thomason's colimit theorem for the double category of elements

Category Theory 2025-06-11 v1 Algebraic Topology

Authors: Andrew Gill , Maru Sarazola

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 $B hocolim F\simeq B(\iint_C F)$ .

Keywords

Thomason colimit theorem double category of elements 2-category 2-functor weak homotopy equivalence homotopy colimit

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@article{arxiv.2506.08246,
  title  = {Thomason's colimit theorem for the double category of elements},
  author = {Andrew Gill and Maru Sarazola},
  journal= {arXiv preprint arXiv:2506.08246},
  year   = {2025}
}

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Thomason's colimit theorem for the double category of elements

Abstract

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