| Résume | In this talk we shall introduce the notion of a new category called the category of superpowersets. Examples superpowersets are found among powersets of nonempty sets, presentable posets in the theory of quadratic forms, and fuzzy subsets of a given set, and we shall see that the category of superpowersets forms a topos. Superpowersets can be equipped with a form of binary operation yielding objects that we shall call superpowergroups. Examples of superpowergroups are naturally built from groups, hypergroups, presentable groups, fuzzy groups and fuzzy hypergroups. The question of when superpowergroups form a topos will be also addressed. |
