  In this paper we provide a geometric derivation of the master loop equation
for the lattice Yang-Mills model with structure group $G \in \{SO(N),SU(N),
U(N)\}$. This approach is based on integration by parts on $G$. In the appendix
we compare our approach to that of \cite{Ch19a} and \cite{J16} based on
Schwinger-Dyson equations, and \cite{SheSmZh22} based on stochastic analysis.
In particular these approaches are all easily seen to be equivalent. The
novelty in our approach is the use of intrinsic geometry of $G$ which we
believe simplifies the derivation.
