In mathematics, a direct limit (also called inductive limit) is a colimit of a "directed family of objects". We will first give the definition for algebraic structures like groups and modules, and then the general definition which can be used in any category.
Read more about Direct Limit: Examples, Related Constructions and Generalizations
Famous quotes containing the words direct and/or limit:
“The most passionate, consistent, extreme and implacable enemy of the Enlightenment and ... all forms of rationalism ... was Johann Georg Hamann. His influence, direct and indirect, upon the romantic revolt against universalism and scientific method ... was considerable and perhaps crucial.”
—Isaiah Berlin (b. 1909)
“Moreover, the universe as a whole is infinite, for whatever is limited has an outermost edge to limit it, and such an edge is defined by something beyond. Since the universe has no edge, it has no limit; and since it lacks a limit, it is infinite and unbounded. Moreover, the universe is infinite both in the number of its atoms and in the extent of its void.”
—Epicurus (c. 341–271 B.C.)