Global element

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In a category theory, a global element of an object A of a category is an arrow

h : 1 → A

where 1 is a terminal object of the category. Global elements allow to partially reconstruct element-wise thinking known from set theory within a cateory. However, the whole is more than the sum of its parts, i.e. an object need not be determined by its global elements (even not up to isomorphism).