These notes
are a current snapshot of the development of the theory of collagories, which
are

defined
essentially as Òdistributive allegories without zero morphismsÓ and named for
their close

relationship
with the adhesive categories currently popular as a foundation for the
categorical

double-pushout
approach to graph transformation.

We argue
that, thanks to their relation-algebraic flavour, collagories provide a more
accessible

and more
flexible setting. One contributing factor to this is that the universal
characterisations

of pushouts
and pullbacks in categories can be replaced with the local characterisations

of
tabulations and co-tabulations in collagories.

We document
accessibility by showing ways to construct collagories of semi-unary algebras,

which allow
natural representations in particular of graph structures, also with fixed
label sets.

Via the
local ordering on homsets, collagories have a simple 2-categorical structure,
and we

use this to
show that co-tabulations are equivalent to lax colimits of difunctional
morphisms,

and
co-tabulations arising from spans of mappings are equivalent to bipushouts,
which satisfy

stronger
conditions than just pushouts of mappings.

Finally, we
consider Van-Kampen squares, the central ingredient of the definition of
adhesive

categories,
and obtain an interesting characterisation of Van-Kampen squares in
collagories.