Work

Thomason’s Colimit Theorem for the Double Category of Elements

Year: 2026

Type: article

Abstract: We show that, for any 2-category $$\mathcal {C}$$ C and 2-functor $$F:\mathcal {C}^\textrm{op}\rightarrow \underline{\textrm{Cat}}$$ F : C op → Cat ̲ , the double category of elements $$\iint _\mathcal {C}F$$ ∬ C F introduced by Grandis and Paré satisfies a version of Thomason’s colimit theorem; that is, there is a weak homotopy equivalence $$B{{\,\mathrm{\textrm{hocolim}}\,}}F\simeq B(\iint _\mathcal {C}F)$$ B hocolim F ≃ B ( ∬ C F ) .

Source: Applied Categorical Structures

DOI: 10.1007/s10485-026-09858-y

Authors: Andrew Gill, Maru Sarazola

Institution: University of Minnesota

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funder: National Science Foundation