In category theory, a global element of an object A from a category is a morphism
where 1 is a terminal object of the category. [1] Roughly speaking, global elements are a generalization of the notion of "elements" from the category of sets, and they can be used to import set-theoretic concepts into category theory. However, unlike a set, an object of a general category need not be determined by its global elements (not even up to isomorphism).
In an elementary topos the global elements of the subobject classifier form a Heyting algebra when ordered by inclusion of the corresponding subobjects of the terminal object. [3] For example, Grph happens to be a topos, whose subobject classifier Ω is a two-vertex directed clique with an additional self-loop (so five edges, three of which are self-loops and hence the global elements of Ω). The internal logic of Grph is therefore based on the three-element Heyting algebra as its truth values.