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 and, small, large and/or categories:
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Your bell-mounted churches, and guardless the sacred cairn and the rath,
And a small and a feeble populace stooping with mattock and spade,
Or weeding or ploughing with faces a-shining with much-toil wet;
While in this place and that place, with bodies unglorious, their chieftains stood....”
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“Child, the current of your breath is six days long.
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—Anne Sexton (1928–1974)
“The newspapers, especially those in the East, are amazingly superficial and ... a large number of news gatherers are either cynics at heart or are following the orders and the policies of the owners of their papers.”
—Franklin D. Roosevelt (1882–1945)
“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)