Topos

Summary

An (elementary) topos is a category with finite limits, exponential objects and a subobject classifier. The category of sets is a topos, and so is the category of sheaves on any site. A topos behaves like a universe of sets in which one can do much of mathematics, but its internal logic is in general intuitionistic. Toposes connect geometry, where they arise as generalized spaces, with logic, where they serve as models of higher-order theories.