  All four of these conditions can be formulated in category-theoretic language — a category satisfying them is called a topos. The category Set is a topos; so also are (i) the category Set(B) of Boolean-valued sets and mappings in any Boolean extension V(B) of the universe of sets; (ii) the category of sheaves of sets on a topological space; (iii) the category of all diagrams of maps of sets