# Diagrammatic globular sets

After recalling quite a bit from Johnson's paper
``The combinatorics of n-categorical pasting''
[J. Pure Appl. Algebra 62 (1989), 211-225] and
the notions of globular cardinal and n-stage tree from
Street's paper ``The petit topos of globular sets'' [Preprint
98/232, Macquarie University], I showed that
the following are equivalent:
- A is a well-formed loop-free pasting scheme all whose
cells are globes,
- A is a diagrammatic globular set,
- A is a globular cardinal,
- A is T
^{*} for some (unique) n-stage tree T.

In this, a *diagrammatic globular set* is a finite
globular set satisfying the following two conditions, which
are easy to check: there is no x with x <| x, and
if s (x) = s (y) or t (x) = t (y) then x = y or there exists
w with t (w) = x or t (w) = y.
See section 5 of the paper ``Teisi in __Ab__''.

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