  This letter reports on a metriplectic formulation of collisional, nonlinear
full-$f$ electromagnetic gyrokinetic theory compliant with energy conservation
and monotonic entropy production. In an axisymmetric background magnetic field,
the toroidal angular momentum is also conserved. Notably, a new collisional
current, contributing to the gyrokinetic Maxwell-Amp\`ere equation and the
gyrokinetic charge conservation law, is discovered.
