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 settheoretic 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). For example, the terminal object of the category Grph of graph homomorphisms has one vertex and one edge, a selfloop,^{[2]} whence the global elements of a graph are its selfloops, conveying no information either about other kinds of edges, or about vertices having no selfloop, or about whether two selfloops share a vertex.
In an elementary topos the global elements of the subobject classifier Ω 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 twovertex directed clique with an additional selfloop (so five edges, three of which are selfloops and hence the global elements of Ω). The internal logic of Grph is therefore based on the threeelement Heyting algebra as its truth values.
A wellpointed category is a category that has enough global elements to distinguish every two morphisms. That is, for each pair of distinct arrows A → B in the category, there should exist a global element whose compositions with them are different from each other.^{[1]}
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Trusses (2/6): Transformation Matrix and the Global Element Stiffness Matrix

Trusses (1/6): Intro, FE Formulation, & Coordinate Systems

Trusses (4/6): Example  Transform Element Matrices and Assemble Global Stiffness Matrix
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References
 ^ ^{a} ^{b} Mac Lane, Saunders; Moerdijk, Ieke (1992), Sheaves in geometry and logic: A first introduction to topos theory, Universitext, New York: SpringerVerlag, p. 236, ISBN 0387977104, MR 1300636.
 ^ Gray, John W. (1989), "The category of sketches as a model for algebraic semantics", Categories in computer science and logic (Boulder, CO, 1987), Contemp. Math., 92, Amer. Math. Soc., Providence, RI, pp. 109–135, doi:10.1090/conm/092/1003198, MR 1003198.
 ^ Nourani, Cyrus F. (2014), A functorial model theory: Newer applications to algebraic topology, descriptive sets, and computing categories topos, Toronto, ON: Apple Academic Press, p. 38, doi:10.1201/b16416, ISBN 9781926895925, MR 3203114.