Small and Large Categories
A category C is called small if both ob(C) and hom(C) are actually sets and not proper classes, and large otherwise. A locally small category is a category such that for all objects a and b, the hom-class hom(a, b) is a set, called a homset. Many important categories in mathematics (such as the category of sets), although not small, are at least locally small.
Read more about this topic: Category (mathematics)
Famous quotes containing the words small and, small, large and/or categories:
“There the wicked cease from troubling, and there the weary are at rest. There the prisoners are at ease together; they do not hear the voice of the taskmaster. The small and the great are there, and the slaves are free from their masters.”
—Bible: Hebrew, Job 3:17-19.
“Small debts are like small shot; they are rattling on every side, and can scarcely be escaped without a wound: great debts are like cannon; of loud noise, but little danger.”
—Samuel Johnson (1709–1784)
“Pigeons on the grass alas.
Pigeons on the grass alas.
Short longer grass short longer longer shorter yellow
grass Pigeons large pigeons on the shorter longer yellow grass
alas pigeons on the grass.”
—Gertrude Stein (1874–1946)
“All cultural change reduces itself to a difference of categories. All revolutions, whether in the sciences or world history, occur merely because spirit has changed its categories in order to understand and examine what belongs to it, in order to possess and grasp itself in a truer, deeper, more intimate and unified manner.”
—Georg Wilhelm Friedrich Hegel (1770–1831)