A theoretical framework shows weak homotopy equivalence in double categories and 2-functors, influencing category theory.
We show that, for any 2-category C C and 2-functor F:Cᵒp→ Cat F : C op → Cat ̲ , the double category of elements CF ∬ C F introduced by Grandis and Paré satisfies a version of Thomason’s colimit theorem; that is, there is a weak homotopy equivalence B\,hocolim\,F B( CF) B hocolim F ≃ B ( ∬ C F ) .
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Gill et al. (2026) studied this question.
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