<p>We show that, for any 2-category <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {C}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">C</mi> </math></EquationSource> </InlineEquation> and 2-functor <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(F:\mathcal {C}^\textrm{op}\rightarrow \underline{\textrm{Cat}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>F</mi> <mo>:</mo> <msup> <mrow> <mi mathvariant="script">C</mi> </mrow> <mtext>op</mtext> </msup> <mo stretchy="false">→</mo> <munder> <mtext>Cat</mtext> <mo>̲</mo> </munder> </mrow> </math></EquationSource> </InlineEquation>, the double category of elements <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\iint _\mathcal {C}F\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mo>∬</mo> <mi mathvariant="script">C</mi> </msub> <mi>F</mi> </mrow> </math></EquationSource> </InlineEquation> introduced by Grandis and Paré satisfies a version of Thomason’s colimit theorem; that is, there is a weak homotopy equivalence <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(B{{\,\mathrm{\textrm{hocolim}}\,}}F\simeq B(\iint _\mathcal {C}F)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>B</mi> <mrow> <mspace width="0.166667em" /> <mtext>hocolim</mtext> <mspace width="0.166667em" /> </mrow> <mi>F</mi> <mo>≃</mo> <mi>B</mi> <mo stretchy="false">(</mo> <msub> <mo>∬</mo> <mi mathvariant="script">C</mi> </msub> <mi>F</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>.</p>