Thomason’s Colimit Theorem for the Double Category of Elements

Andrew Gill; Maru Sarazola

doi:10.1007/s10485-026-09858-y

Thomason’s Colimit Theorem for the Double Category of Elements

Andrew Gill
, Maru Sarazola

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We show that, for any 2-category C and 2-functor F:Cop→Cat̲, the double category of elements ∬CF introduced by Grandis and Paré satisfies a version of Thomason’s colimit theorem; that is, there is a weak homotopy equivalence BhocolimF≃B(∬CF).

Original language	English (US)
Article number	20
Journal	Applied Categorical Structures
Volume	34
Issue number	3
DOIs	https://doi.org/10.1007/s10485-026-09858-y
State	Published - Jun 2026

Bibliographical note

Publisher Copyright:
© The Author(s) 2026.

Keywords

Category of elements
Double categories
Grothendieck construction
Homotopy colimit
Thomason’s theorem

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10.1007/s10485-026-09858-y

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abstract = "We show that, for any 2-category C and 2-functor F:Cop→Cat̲, the double category of elements ∬CF introduced by Grandis and Par{\'e} satisfies a version of Thomason{\textquoteright}s colimit theorem; that is, there is a weak homotopy equivalence BhocolimF≃B(∬CF).",

keywords = "Category of elements, Double categories, Grothendieck construction, Homotopy colimit, Thomason{\textquoteright}s theorem",

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N2 - We show that, for any 2-category C and 2-functor F:Cop→Cat̲, the double category of elements ∬CF introduced by Grandis and Paré satisfies a version of Thomason’s colimit theorem; that is, there is a weak homotopy equivalence BhocolimF≃B(∬CF).

AB - We show that, for any 2-category C and 2-functor F:Cop→Cat̲, the double category of elements ∬CF introduced by Grandis and Paré satisfies a version of Thomason’s colimit theorem; that is, there is a weak homotopy equivalence BhocolimF≃B(∬CF).

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KW - Double categories

KW - Grothendieck construction

KW - Homotopy colimit

KW - Thomason’s theorem

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Thomason’s Colimit Theorem for the Double Category of Elements

Abstract

Bibliographical note

Keywords

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