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:
“If I’m not so large as you,
You are not so small as I,
And not half so spry.”
—Ralph Waldo Emerson (1803–1882)
“Cannot people realize how large an income is thrift?”
—Marcus Tullius Cicero (106–43 B.C.)
“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)