Ensembles reguliers

Abstract

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.