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\section{Introduction}  \label{sec:Introduction}  The design study of Future Circular Colliders (FCC) in a 100-km ring in the Geneva area has started at CERN at the beginning of 2014, as an option for a post-LHC particle accelerators. The study has an emphasis on proton-proton and electron-positron high-energy frontier machines~\cite{FCCWebSite}. The first step of the FCC physics programme would make use of an the  ${\rm e^+e^-}$ collider, now  called FCC-ee and formerly known as TLEP, with centre-of-mass energies ranging from the Z pole to the ${\rm t\bar t}$ threshold and beyond. A first look at the physics case of the FCC-ee can be found in Ref.~\cite{Bicer_2014}. The only aspect of the top-quark physics summarized in this first look concerns the precision measurements of the top-quark mass, width and Yukawa coupling through a scan of the ${\rm t\bar t}$ production threshold, with $\sqrt{s}$ comprised between~340 and~350\,GeV. The expected precision of top-quark mass is in turn used in a global electroweak fit to set constraints on new physics coupled to gauge bosons up to a scale of 100\,TeV. Although not alluded to in the first look, new physics might also show up through deviations of the top-quark couplings to gauge bosons with respect to their standard-model predictions. Theories in which the top-quark and the Higgs boson are composite would lead to such deviations. While these theories also lead to modifications of the Higgs boson couplings and of the Z decay width, it is not unlikely that the inclusion of a direct measurement of the ttZ coupling in the global electroweak fit further constrain these theories.