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, large and/or categories:
“A little quaker, the whole body of him trembling,
His absurd whiskers sticking out like a cartoon-mouse,
His feet like small leaves,
Little lizard-feet,
Whitish and spread wide when he tried to struggle away,”
—Theodore Roethke (1908–1963)
“Why are there trees I never walk under but large and melodious thoughts descend upon me?”
—Walt Whitman (1819–1892)
“The analogy between the mind and a computer fails for many reasons. The brain is constructed by principles that assure diversity and degeneracy. Unlike a computer, it has no replicative memory. It is historical and value driven. It forms categories by internal criteria and by constraints acting at many scales, not by means of a syntactically constructed program. The world with which the brain interacts is not unequivocally made up of classical categories.”
—Gerald M. Edelman (b. 1928)