  In this exposition we highlight product systems as the semigroup analogue of
Fell bundles. Motivated by Fock creation operators we extend the definition of
Fowler's product systems over unital discrete left-cancellative semigroups, via
both a concrete and an abstract characterization. We next underline the
importance of Fock spaces and Fell bundle methods for obtaining covariant
representation results. First, the strongly covariant representations of
Sehnem, for product systems over group embeddable semigroups, find their
analogue here. Secondly, we give two solutions for the existence of the
co-universal C*-algebra with respect to equivariant injective Fock-covariant
representations in this context. The first one uses an intertwining isometry
technique to realize it as the C*-envelope of the normal cosystem on the Fock
tensor algebra. The second uses a Fell bundle quotient technique to realize it
as the reduced C*-algebra of Sehnem's strong covariance relations. This
C*-algebra is boundary for a larger class of equivariant injective
representations.
