  We provide a construction for holes into which morphisms of abstract
symmetric monoidal categories can be inserted, termed the polyslot construction
pslot[C], and identify a sub-class srep[C] of polyslots that are single-party
representable. These constructions strengthen a previously introduced notion of
locally-applicable transformation used to characterize quantum supermaps in a
way that is sufficient to re-construct unitary supermaps directly from the
monoidal structure of the category of unitaries. Both constructions furthermore
freely reconstruct the enriched polycategorical semantics for quantum supermaps
which allows to compose supermaps in sequence and in parallel whilst forbidding
the creation of time-loops. By freely constructing key compositional features
of supermaps, and characterizing supermaps in the finite-dimensional case,
polyslots are proposed as a suitable generalization of unitary-supermaps to
infinite dimensions and are shown to include canonical examples such as the
quantum switch. Beyond specific applications to quantum-relevant categories, a
general class of categorical structures termed path-contraction groupoids are
defined on which the srep[C] and pslot[C] constructions are shown to coincide.
