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, large and/or categories:
“Ill-weaved ambition, how much art thou shrunk!
When that this body did contain a spirit,
A kingdom for it was too small a bound,
But now two paces of the vilest earth
Is room enough.”
—William Shakespeare (1564–1616)
“Why are there trees I never walk under but large and melodious thoughts descend upon me?”
—Walt Whitman (1819–1892)
“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)