  As an example of the categorical apparatus of pseudo algebras over
2-theories, we show that pseudo algebras over the 2-theory of categories can be
viewed as pseudo double categories with folding or as appropriate 2-functors
into bicategories. Foldings are equivalent to connection pairs, and also to
thin structures if the vertical and horizontal morphisms coincide. In a sense,
the squares of a double category with folding are determined in a functorial
way by the 2-cells of the horizontal 2-category. As a special case, strict
2-algebras with one object and everything invertible are crossed modules under
a group.
