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.
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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.
“A little quaker, the whole body of him trembling,
His absurd whiskers sticking out like a cartoon-mouse,
His feet like small leaves,
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