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.
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“I, who travel most often for my pleasure, do not direct myself so badly. If it looks ugly on the right, I take the left; if I find myself unfit to ride my horse, I stop.... Have I left something unseen behind me? I go back; it is still on my road. I trace no fixed line, either straight or crooked.”
—Michel de Montaigne (1533–1592)
“No one who cannot limit himself has ever been able to write.”
—Nicolas Boileau-Despréaux (1636–1711)