Definition 0.1
Superdiagrams 
are defined as heterofunctors

that are subject to
ETAS axioms
and link
categorical diagrams

(regarded as (homo
)functors, which are subject to the eight
ETAC axioms) in a manner similar to how
groupoids
are being constructed as
many-object structures of linked groups with all invertible morphisms between the linked groups. Thus, in the supercategory definition-instead of a groupoid with all invertible morphisms- one replaces the linked groups by several

's linked by hetero-functors

between such categorical diagrams or
categorical sequences
with different structure. The heterofunctors corresponding to
superdiagrams also need not be invertible (as in the case of
supergroupoid structures). In this construction, one defines a supercategorical
diagram
in terms of the
composition
“

” of the heterofunctors

with the (homo)functors

determined by

, so that
the right hand side of this equation is to be interpreted as a heterofunctor acting on the (homo)functor(s)

determined by the categorical diagram, or the categorical sequence,

.