  It is well known that BRST symmetry plays a fundamental role in constructing
quantum gauge theories. Yet, at the classical level, it constitutes the modern
language to study constrained systems. First, this letter reviews the Sp(2)
covariant quantisation of gauge theories, so that the geometrical
interpretation of gauge theories in terms of quasi-principal fibre bundles
Q(Ms, Gs) is the main scenario. It is then described the Sp(2) algebra for
ordinary Yang-Mills theory. Some basic set theory and topology terms are
reviewed to proceed then to use theorems on left inverse and right inverse of
functions together with groups (Ms, Gs) to have triangular compositions of
functions on manifolds. Henceforth, it is so the purpose of this letter to
present topological structures to gauge theories, in particular to construct
commutative diagrams for cocycle conditions of the Sp(2) symmetry.
