As indicated in the introduction, sheaves on ordinary topological spaces motivate many of the basic definitions and results of topos theory. The category of sets is an important special case: it plays the role of a point in topos theory. Indeed, a set may be thought of as a sheaf on a point. More exotic examples, and the "raison d'être" of topos theory, come from algebraic geometry. To a scheme and even a stack one may associate an étale topos, an fppf topos, a Nisnevich topos... Another important example of a topos is from the crystalline site. Topos theory is, in some sense, a generalization of classical point-set topology. One should therefore expect to see old and new instances of pathological behavior. For instance, there is an example due to Pierre Deligne of a nontrivial topos that has no points (see below for the definition of points of a topos). If "X" and "Y" are topoi, a "geometric morphism" is a pair of adjoint functors ("u"∗,"u"∗) (where "u"∗ : "Y" → "X" is left adjoint to "u"∗ : "X" → "Y") such that "u"∗ preserves finite limits. Note that "u"∗ automatically preserves colimits by virtue of having a right adjoint. By Freyd's adjoint functor theorem, to give a geometric morphism "X" → "Y" is to give a functor "u"∗: "Y" → "X" that preserves finite limits and all small colimits. Thus geometric morphisms between topoi may be seen as analogues of maps of locales. If "X" and "Y" are topological spaces and "u" is a continuous map between them, then the pullback and pushforward operations on sheaves yield a geometric morphism between the associated topoi. A point of a topos "X" is defined as a geometric morphism from the topos of sets to "X". If "X" is an ordinary space and "x" is a point of "X", then the functor that takes a sheaf "F" to its stalk "Fx" has a right adjoint (the "skyscraper sheaf" functor), so an ordinary point of "X" also determines a topos-theoretic point.