High-resolution Very-Long-Baseline Interferometry observations of relativistic jets are essential to constrain fundamental parameters of jet formation models. At a distance of 249 Mpc, Cygnus A is a unique target for such studies, being the only Fanaroff-Riley Class II radio galaxy for which a detailed sub-parsec scale imaging of the base of both jet and counter-jet can be obtained. Observing at millimeter wavelengths unveils those regions which appear self-absorbed at longer wavelengths and enables an extremely sharp view towards the nucleus to be obtained. We performed 7 mm Global VLBI observations, achieving ultra-high resolution imaging on scales down to 90 $mu$as. This resolution corresponds to a linear scale of only ${sim}$400 Schwarzschild radii (for $M_{mathrm{BH}}=2.5 times 10^9 M_{odot}$). We studied the kinematic properties of the main emission features of the two-sided flow and probed its transverse structure through a pixel-based analysis. We suggest that a fast and a slow layer, with different acceleration gradients, exist in the flow. The extension of the acceleration region is large (${sim} 10^4 R_{mathrm{S}}$), indicating that the jet is magnetically-driven. The limb brightening of both jet and counter-jet and their large opening angles ($phi_mathrm{J}{sim} 10^{circ}$) strongly favor a spine-sheath structure. In the acceleration zone, the flow has a parabolic shape ($rpropto z^{0.55pm 0.07}$). The acceleration gradients and the collimation profile are consistent with the expectations for a jet in equilibrium (Lyubarsky 2009), achieved in the presence of a mild gradient of the external pressure ($ppropto z^{-k}, kleq2$).}
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