  We define an interesting sub-category of the category of simplicial sets,
$\Sr$, whose objects are called regular. Both it and the subcategory ${\cal
S}_{f-{\rm reg}}$ of finite regular simplicial sets have good stability
properties under limits and union. The category ${\cal S}_{f-{\rm reg}}$ is
cartesian closed, in contrast to the category of finite simplicial sets which
is not cartesian closed.
