for disambiguation see wreath product
objects are -tuples of objects of , for any ;
morphisms are tuples
a morphism in ;
morphisms for and .
An object of is to be thought of as a sequence of morphisms labeled by objects of
and morphisms are given by maps between these linear orders equipped with morphisms from the th object in the source to all the objects in the target that sit in between the image of the th step.
Section 3 of