Composite Higgs models and $t\bar t$ production at future $e^+e^-$ colliders

The study of the top quark properties will be an integral part of any particle physics activity at future leptonic colliders. In this proceeding we discuss the possibility of testing composite Higgs scenarios at $e^+e^-$ prototypes through deviations from the Standard Model predictions in $t\bar t$ production observables for various centre of mass energies, ranging from 370 GeV up to 1 TeV. This proceedings draws from Ref. arXiv:1504.05407