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:
“Thirty-five years ago, when I was a college student, people wrote letters. The businessman who read, the lawyer who traveled; the dressmaker in evening school, my unhappy mother, our expectant neighbor: all conducted an often large and varied correspondence. It was the accustomed way of ordinarily educated people to occupy the world beyond their own small and immediate lives.”
—Vivian Gornick (b. 1935)
“We must remain as close to the flowers, the grass, and the butterflies as the child is who is not yet so much taller than they are. We adults, on the other hand, have outgrown them and have to lower ourselves to stoop down to them. It seems to me that the grass hates us when we confess our love for it.—Whoever would partake of all good things must understand how to be small at times.”
—Friedrich Nietzsche (1844–1900)
“Whenever you pray, make sure you do it at school assemblies and football games, like the demonstrative creatures who pray before large television audiences. That is the real goal of the thing. But do not, I urge you, pray all alone in your home where no one can see. That does not get you ratings.”
—Garry Wills (b. 1934)
“Kitsch ... is one of the major categories of the modern object. Knick-knacks, rustic odds-and-ends, souvenirs, lampshades, and African masks: the kitsch-object is collectively this whole plethora of “trashy,” sham or faked objects, this whole museum of junk which proliferates everywhere.... Kitsch is the equivalent to the “cliché” in discourse.”
—Jean Baudrillard (b. 1929)