ABSTRACT
Topos, plural “topoi” or “toposes”, is a type of category that behaves like the category of sheaves of sets on a topological space (or more generally: on a site). A typical example is the Grothendieck topoi that have applications in algebraic geometry and sets. Since the introduction of sheaves into mathematics in the 1940s a major theme has been to study a space by studying sheaves on a space. This idea was carried onto what is called Grothendieck topos. The main utility of this notion is in the abundance of situations in mathematics where topological intuition is very effective but a natural topological space is lacking. The single success of this programmatic idea has been the introduction of the étale topos of a scheme.
