jats:titleAjats:scbstract</jats:sc> </jats:title>jats:pWe report on the calculation of the next-to-leading order QCD corrections to the production of a jats:inline-formulajats:alternativesjats:tex-math$$ t\overline{t} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mit</mml:mi> mml:mover mml:mit</mml:mi> mml:mo¯</mml:mo> </mml:mover> </mml:math></jats:alternatives></jats:inline-formula> pair in association with two heavy-flavour jets. We concentrate on the di-lepton jats:inline-formulajats:alternativesjats:tex-math$$ t\overline{t} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mit</mml:mi> mml:mover mml:mit</mml:mi> mml:mo¯</mml:mo> </mml:mover> </mml:math></jats:alternatives></jats:inline-formula> decay channel at the LHC with jats:inline-formulajats:alternativesjats:tex-math$$ \sqrt{s} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:msqrt mml:mis</mml:mi> </mml:msqrt> </mml:math></jats:alternatives></jats:inline-formula> = 13 TeV. The computation is based on jats:italicpp</jats:italic> → jats:italice</jats:italic>jats:sup+</jats:sup>jats:italicν</jats:italic>jats:subjats:italice</jats:italic></jats:sub>jats:italicμ</jats:italic>jats:supjats:italic−</jats:italic></jats:sup>jats:inline-formulajats:alternativesjats:tex-math$$ \overline{\nu} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mover mml:miν</mml:mi> mml:mo¯</mml:mo> </mml:mover> </mml:math></jats:alternatives></jats:inline-formula>jats:subjats:italicμ</jats:italic></jats:sub>jats:inline-formulajats:alternativesjats:tex-math$$ b\overline{b}b\overline{b} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mib</mml:mi> mml:mover mml:mib</mml:mi> mml:mo¯</mml:mo> </mml:mover> mml:mib</mml:mi> mml:mover mml:mib</mml:mi> mml:mo¯</mml:mo> </mml:mover> </mml:math></jats:alternatives></jats:inline-formula> matrix elements and includes all resonant and non-resonant diagrams, interferences and off-shell effects of the top quark and the jats:italicW</jats:italic> gauge boson. As it is customary for such studies, results are presented in the form of inclusive and differential fiducial cross sections. We extensively investigate the dependence of our results upon variation of renormalisation and factorisation scales and parton distribution functions in the quest for an accurate estimate of the theoretical uncertainties. We additionally study the impact of the contributions induced by the bottom-quark parton density. Results presented here are particularly relevant for measurements of jats:inline-formulajats:alternativesjats:tex-math$$ t\overline{t}H $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mit</mml:mi> mml:mover mml:mit</mml:mi> mml:mo¯</mml:mo> </mml:mover> mml:miH</mml:mi> </mml:math></jats:alternatives></jats:inline-formula>(jats:italicH</jats:italic> → jats:inline-formulajats:alternativesjats:tex-math$$ b\overline{b} $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mib</mml:mi> mml:mover mml:mib</mml:mi> mml:mo¯</mml:mo> </mml:mover> </mml:math></jats:alternatives></jats:inline-formula>) and the determination of the Higgs coupling to the top quark. In addition, they might be used for precise measurements of the top-quark fiducial cross sections and to investigate top-quark decay modelling at the LHC.</jats:p>