I will discuss a general notion of algebraic gauge theory obtained via extracting the main properties of classical gauge theory. Building on a previous work on transferring curved A-structures, I will show that under certain technical conditions, algebraic gauge theories can be transferred along chain contractions. Specializing to the case of the contraction from differential forms to cochains, one obtains a simplicial gauge theory on the matrix-valued simplicial cochains of a triangulated manifold. In particular, one obtains discrete notions of connection, curvature, gauge transformation and gauge invariant action. Time permitting, I will also discuss possible applications to constructive quantum Yang-Mills theory.